Introducción al cálculo fraccional y q-fraccional : con aplicaciones

Este libro contiene elementos importantes tanto del cálculo fraccional como del q-fraccional. Está diseñado para profesionales en Matemáticas, Física y ciencias de Ingenierías que deseen tener una primera aproximación a estas teorías. Su contenido está distribuido de la siguiente manera: En el prime...

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Autores:
Castillo Pérez, Jaime
Tipo de recurso:
Book
Fecha de publicación:
2020
Institución:
Universidad de la Guajira
Repositorio:
Repositorio Uniguajira
Idioma:
spa
OAI Identifier:
oai:repositoryinst.uniguajira.edu.co:uniguajira/741
Acceso en línea:
https://repositoryinst.uniguajira.edu.co/handle/uniguajira/741
Palabra clave:
Cálculo
Funciones
Análisis funcional
Teoría de los operadores
Rights
openAccess
License
Copyright - Universidad de La Guajira, 2020
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oai_identifier_str oai:repositoryinst.uniguajira.edu.co:uniguajira/741
network_acronym_str Uniguajra2
network_name_str Repositorio Uniguajira
repository_id_str
dc.title.spa.fl_str_mv Introducción al cálculo fraccional y q-fraccional : con aplicaciones
title Introducción al cálculo fraccional y q-fraccional : con aplicaciones
spellingShingle Introducción al cálculo fraccional y q-fraccional : con aplicaciones
Cálculo
Funciones
Análisis funcional
Teoría de los operadores
title_short Introducción al cálculo fraccional y q-fraccional : con aplicaciones
title_full Introducción al cálculo fraccional y q-fraccional : con aplicaciones
title_fullStr Introducción al cálculo fraccional y q-fraccional : con aplicaciones
title_full_unstemmed Introducción al cálculo fraccional y q-fraccional : con aplicaciones
title_sort Introducción al cálculo fraccional y q-fraccional : con aplicaciones
dc.creator.fl_str_mv Castillo Pérez, Jaime
dc.contributor.author.none.fl_str_mv Castillo Pérez, Jaime
dc.subject.lemb.none.fl_str_mv Cálculo
Funciones
Análisis funcional
Teoría de los operadores
topic Cálculo
Funciones
Análisis funcional
Teoría de los operadores
description Este libro contiene elementos importantes tanto del cálculo fraccional como del q-fraccional. Está diseñado para profesionales en Matemáticas, Física y ciencias de Ingenierías que deseen tener una primera aproximación a estas teorías. Su contenido está distribuido de la siguiente manera: En el primer capítulo se presentan algunos elementos de cálculo fraccional, inicialmente se hace un recorrido sobre el desarrollo histórico del mismo, desde sus inicios hacia el siglo XVII hasta la fecha. Se presentan algunas definiciones y se muestran los operadores más usuales de dicho cálculo. En el segundo capítulo se presentan las funciones más usadas en el cálculo fraccional, entre las que se cuentan a la función gamma, función gamma incompleta, función beta, función hipergeométrica generalizada, función hipergeométrica de Fox-Wright, función H, funciones de Mittag-Leffler, función de Agarwal, función de Erd`elyi, función de Robotnov-Hartley, funciónde Miller-Ross, funciones generalizadas de seno y coseno, funciones de Bessel. Se muestran algunas aplicaciones del operador derivada fraccional de Riemann-Liouville a una variedad de funciones. En el tercer capítulo se presentan los operadores de integración fraccional establecidos por varios investigadores en este campo y se muestran algunas aplicaciones. Introducción al cálculo fraccional y q-fraccional2 En el cuarto capítulo se hace una breve reseña histórica del cálculo q-fraccional, se define la q-derivada, la q-integral y varios conceptos que soportan el desarrollo de este campo de la matemática. En el quinto capítulo se presentan las funciones usadas en el cálculo q-fraccional, las cuales se establecen como análogas básicas de las funciones factorial, gamma, beta, hipergeométrica, exponencial, Bessel, H, Wright. Se introduce un nuevo teorema donde se establece la convergencia absoluta para la análoga básica de la función hipergeométrica de Fox-Wright. En el sexto capítulo se presentan los operadores q-fraccionales con sus reglas de composición y ciertas aplicaciones a las q-funciones
publishDate 2020
dc.date.issued.none.fl_str_mv 2020
dc.date.accessioned.none.fl_str_mv 2023-07-27T20:51:45Z
dc.date.available.none.fl_str_mv 2023-07-27T20:51:45Z
dc.type.spa.fl_str_mv Libro
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_2f33
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/book
dc.type.redcol.spa.fl_str_mv https://purl.org/redcol/resource_type/LIB
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.isbn.spa.fl_str_mv 9789585178199
dc.identifier.uri.none.fl_str_mv https://repositoryinst.uniguajira.edu.co/handle/uniguajira/741
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dc.relation.references.spa.fl_str_mv Abel, N.H., Resolution d’un probl`eme de mecanique; Oeuvres Compl`etes, 1, 27-30 (1823).
Abel, N.H., Sur quelques int´egrales d´efinies; Oeuvres Compl`etes, 1, 93-102 (1825).
Agarwal, R. P., A q-analogue of MacRobert’s generalized E-function; Ganita, 11, 49-63 (1960).
Agarwal, R. P., Generalized Hypergeometric Series, Asia Publishing House, Bombay, New York,USA, (1963).
Agarwal, R. P., Certain fractional q-integrals and q-derivatives; Proc. Camb. Phil. Soc., 66, 365-370 (1969).
Agarwal, R. P.; M. Benchohra y S. Hamani, Boundary value problems for fractional differential equations; Georgian Mathematical Journal, 16(3), 401-411 (2009).
Al-Salam, W. A., q-Analogues of Cauchy’s formula; Proc. Am. Math. Soc., 17, 182-184 (1952-1953).
Al-Salam, W. A., Some fractional q-integrals and q-derivatives; Proc. Edin. Math. Soc., 2(15), 135-140 (1966).
Anastassiou, G. A., Fractional Differentiation Inequalities, Springer, New York, USA, (2009).
Anastassiou, G. A., Advances on Fractional Inequalities, Springer, New York, USA, (2011).
Andrews, G. E., A simple proof of Jacobi’s triple product identity; Proc. Amer. Math. Soc., 16, 333-334 (1965).
Andrews, G. E., On basic hypergeometric series, mock theta functions, and partitions I; Quart. J. Math., 2(17), 64-80 (1966).
Andrews, G. E., On basic hypergeometric series, mock theta functions, and partitions II; Quart. J. Math., 2(17), 132-143 (1966).
] Andrews, G. E., q-identities of Auluck, Carlitz, and Rogers; Duke Math. J., 33, 575-581 (1966).
Andrews, G. E., On q-difference equations for certain well-poised basic hypergeometric series; Quart. J. Math., 2(19), 433-447 (1968).
Andrews, G. E., On Ramanujan’s summation of 1ψ1 (a;b;z); Proc. Amer. Math. Soc., 22, 552-553 (1969).
Annaby, M. H. y Z. S. Mansour, q-Fractional Calculus and Equations, Springer, New York, USA, (2012).
Bagley, R. L. y P. J. Torvik, On the fractional calculus model of viscoelastic behaviour; J. Rheol., 30(1), 133 -155 (1986).
Bagley, R. L., On the fractional order initial value problem and its engineering applications; In Frational Calculus and Its Applications, Koriyama, Japan, Nihon University, pp 11-20 (1990).
Belarbi, S. y Z. Dahmani, On some new fractional integral inequalities; Int. Journal of Math. Analysis, 4(4), 185-191 (2010).
Belavin, V. A.; R. Sh. Nigmatullin y otros dos autores, Fractional differentiation of oscillographic polarograms by means of an electrochemical two-terminal network; Trudy Kazan. Aviation. Inst., 5, 144-152 (1964).
Boole, G., On a general method in analysis; Philos. Trans. Roy. Soc., 134, 225-282 (1844).
Bourlet, M. C., Sur les op´erations en g´en´eral et les ´equations diff´erentielles lin´eaires d’ordre infini; Annales scientifiques de l’´E.N.S., 3(14), 133-190 (1897).
Caputo, M., Linear models of dissipation whose Q is almost frequency independent II; Geophis, J. R. Astr. Soc., 13, 529 - 539 (1967).
Caputo, M., Elasticit´a e Dissipazione, Zanichelli Publisher, Bologna, Italy (1969).
Carlitz, L., Some polynomials related to theta functions; Annali di Matematica pura ed Applicata, 4(41), 359-373 (1955).
Carlitz, L., A q-analogue of a formula of Toscano; Boll. Unione Math. Ital., 12, 414-417 (1957).
Carpinteri, A. y F. Mainardi (Eds.), Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics, Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien, Austria (1997).
Carson, J. R., The Heaviside operational calculus; Bull. Amer. Math. Soc., 32(1), 43-68 (1926).
Cauchy, A. L., M´emoire sur les fonctions dont plusieurs valeurs sont li´ees entre elles par une ´equation lin´eaire, et sur diverses transformations de produits compos´es d’un nombre ind´efini de facteurs; C. R. Acad. Sci. Paris, T. XVII, p. 523, Oeuvres de Cauchy, 1re s´erie, T. VIII, Gauthier-Villars, 42-50 (1843, 1893).
Choi, J.; D. Ritelli y P. Agarwal, Some new inequalities involving Generalized Erd´erlyiKober fractional q-integral operator; Appl. Math. Sci., 9(72), 3577-3591 (2015).
Dahmani, Z.; L. Tabharit y S. Taf, New generalisations of Gru¨ss inequality using RiemannLiouville fractional integrals; Bulletin of Math. Anal. and Applic., 2(3), 93-99 (2010).
Dahmani, Z. y A. Benzidane, New weighted Gru¨ss type inequalities via (α,β) fractional q-integral inequalities; International Journal of Innovation and Applied Studies, 1(1), 76-83 (2012).
Dalir, M. y M. Bashour, Applications of fractional calculus; Applied Mathematical Sciences, 4(21), 1021-1032 (2010).
Das, S., Functional Fractional Calculus, 2 ed., Springer-Verlag Berlin Heidelberg, New York, USA (2011).
Davis, H. D., The Theory of Linear Operators, Principia Press, Bloomington Indiana, USA (1936).
Delgado, M. y L. Galu´e, Fractional q-integral operator involving basic hypergeometric function; Algebras Groups Geom., 25, 53-74 (2008).
Diethelm, K., The Analysis of Fractional Differential Equations, Springer, New York, USA (2010).
Dixon, A. C., Summation of a certain series; Proc. London math. Soc., 1(35), 285-289 (1903).
Dougall, J., On Vandermonde’s theorem and some more general expansions; Proc. Edin. math. Soc., 25, 114-132 (1907).
Dragomir, S. S., A generalization of Gru¨ss inequality in inner product spaces and applications; Journal of Math. Anal. and Applic., 237(1), 74-82 (1999).
Dragomir, S. S., A Gru¨ss type inequality for sequences of vectores in inner product spaces and applications; Journal of Inequalities in Pure and Applied Math., 1(2), 1-11 (2000).
Dragomir, S. S., Some integral inequalities of Gru¨ss type; Indian Journal of Pure and Applied Mathematics, 31(4), 397-415 (2000).
Erd´elyi, A., Transformation of hypergeometric integrals by means of fractional integration by parts; Quart. J. Math. (Oxford), 10, 176-189 (1939).
Erd´elyi, A., On fractional integration and its applications to the theory of Hankel transform; Quart. J. Math. (Oxford), 11(1), 293-303 (1940).
Erd´elyi, A.; W. Magnus y otros dos, Tables of Integral Transforms Vol. II, McGraw-Hill, New York, USA (1954).
Erd´elyi, A., An integral equation involving Legendre functions; SIAM J. Appl. Math., 12, 15-30 (1964).
Erd´elyi, A., Axially symmetric potentials and fractional integration; J. Appl. Math., 13(1), 216-228 (1965).
Ernst, T., The History of q-Calculus and a new Method (Licentiate Thesis), Department of Mathematics of Uppsala University, Uppsala, Suecia (2002).
Euler, L., M´emoire dans le tome V des Comment, Saint Petersberg Ann´ees, 55 (1730).
Galu´e, L. y S. L. Kalla, Operadores integrales que involucran funciones cil´ındricas incompletas; Rev. T´ec. Ing. Univ. Zulia, 11(2), 111-119 (1988).
Galu´e, L., Generalized Erd´erlyi-Kober fractional q-integral operator; Kuwait J. Sci. Eng., 36(2A), 21-34 (2009).
Galu´e, L., Generalized Weyl fractional q-integral operator; Algebras Groups and Geometries, 26, 163-178 (2009).
Galu´e, L., On composition of fractional q−integral operators involving basic hipergeometric functions; Journal of Inequalities and Special Functions, 1(1), 39-52 (2010).
Galu´e, L., Unification of q-fractional integral operator; Algebras Groups and Geom., 28, 283-298 (2011).
Galu´e, L., Unified fractional q-integral operator of q-special functions; Algebras Groups and Geom., 28, 185-204 (2011).
Galu´e, L., Some results on a fractional q-integral operator involving generalized basic hypergeometric function; Rev. T´ec. Ing. Univ. Zulia, 35(3), 302 -310 (2012).
Galu´e, L., Some results involving generalized Erd´erlyi-Kober fractional q-integral operator; Rev. Tecnociet´ıfica URU, 6, 77-89 (2014).
Garg, M. y L.Chanchlani, q-Analogues of Saigo’s fractional calculus operators; Bulletin of Mathematical Analysis and Applications, 3(4), 169-179 (2011).
Garg, M. y L. Chanchlani, Kober fractional q-derivative operators; Le Matematiche, 66(1), 13-26 (2011).
Gasper, G. y M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, New York, USA (2004).
Gauchman, H., integral inequalities in q-calculus; Computers and Mathematics with Applications, 47(2-3), 281-300 (2004).
Gauss, C. F., Disquisitiones generales circa seriem infinitam 1+ αβ γ·1 +...; Comm. soc. reg. sci. G¨ott. rec., Vol. II. Reprinted in Werke, 3 123-162 (1813, 1876).
Gemant, A., A method of analyzing experimental results obtained from elastoviscous bodies; Physics, 7, 311-317 (1936).
Graham, A.; G. W. Scott Blair y R. F. J. Whiters, A methodological problem in rheology; British J. Philos. Sci., 11(44), 265-278 (1961).
Grenness, M. y K. B. Oldham, Semiintegral electroanalysis: theory and verification; Ana. Chem., 44, 1121-1139 (1972).
Gru¨nwald, A. K., Uber begrenzte derivationen und deren anwendung; Z. Angew. Math. Phys., 12, 441-480 (1867).
Gru¨ss, D., ¨Uber das maximum des absoluten Betrages von 1 (b−a) b a f (x)g (x)dx − 1 (b−a)2 b a f (x)dx b a g (x)dx; Math. Z. 39, 215-226 (1935).
Gupta, K. y A. Gupta, Study of modified ¯ H−Transform and generalized fractional integral operator of Weyl type; Int. J. Pure Appl. Sci. Technol., 7(1), 59-67 (2011).
Hahn, W., ¨Uber die h¨oheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen; Math. Nachr., 3, 257-294 (1950).
Hahn, W., ¨Uber uneigentliche L¨osungen linearer geometrischer differenzengleichungen; Math. Annalen, 125, 67-81 (1952).
Hahn, W., Die mechanische Deutung einer geometrischen Differenzengleichung; Zeitschr. angew. Math. Mech., 33, 270-272 (1953).
Hardy, G. H., Notes on some points in the integral calculus; Messenger of Math., 47, 145-150 (1917).
Hardy, G. H. y J. E. Littlewood, Some properties of fractional integrals; Proc. London Math. Soc., 2(24), 37-41 (1925).
Hardy, G. H. y J. E. Littlewood, Some properties of fractional integrals I; Math. Z., 27, 565-606 (1928).
Hardy, G. H. y J. E. Littlewood, Some properties of fractional integrals II; Math. Z., 34, 403-439 (1932).
Heaviside, O., Electrical papers, Macmillan, London, England (1892).
Heaviside, O., On operators in physical mathematics; Proc. Roy. Soc., 504-529 (1893).
Heaviside, O., Electromagnetic Theory, Vol. I, The electrician printing and publishing company, Ltd., London, England (1893).
Heaviside, O., On operators in physical mathematics; Proc. Roy. Soc., 54, 105-143 (1894).
Heaviside, O., Electromagnetic Theory, Vol. II, The electrician printing and publishing company, Ltd., London, England (1920).
Heine, E., ¨Uber die Reihe 1 + [(1−qα) 1−qβ ]/[(1−q)(1−qγ)] x + [(1−qα)(1−qα+1) 1−qβ 1−qβ+1 ]/[(1−
Heine, E., Untersuchungen u¨ber die Reihe 1 + [(1−qα) 1−qβ ]/[(1−q)(1−qγ)] x+ [(1−qα)(1−qα+1) 1−qβ 1−qβ+1 ]/ [(1−q)(1−q2)(1−qγ)(1−qγ+1)]}x2 + ...; J. reine angew. Math. 34, 285-328 (1847).
Heine, E., Handbuch der Kugelfunctionen, Theorie und Anwendungen, vol. 1, Berlin, Germany (1878).
Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific publishing, New Jersey, USA (2000).
Higgins, T. P., The Use of Fractional Integral Operators for Solving Nonhomogeneous Differential Equations, Document DI-82-0677, Boeing Sci. Res. Lab., Washington, USA (1967).
Holmgren, H. J., Om differentialkalkylen med indices of hvad nature sam helst Kongliga svenska; Vetenskaps-akademiens handlinger, 5(11), 1-83 (1864).
Isogawa S., N. Kobachi y S. Hamada, A q-analogue of Riemann-Liouville fractional derivative; Res. Rep. Yatsushiro Nat. Coll. Tech., 29, 59-68 (2007).
Jackson, F. H., A generalization of the functions Γ(n) and xn; Proc. Roy. Soc., 74, 64-72 (1904).
Jackson, F. H., The application of basic numbers to Bessel’s and Legendre’s functions; Proc. Lond. Math. Soc., 32, 1–23 (1905).
Jackson, F. H., On q-functions and a certain difference operator; Trans. Roy. Soc. Edin., 46, 253-281 (1908).
Jackson, F. H., On q-definite integrals; Quart. J. Pure and Appl. Math., 41, 193-203 (1910).
Jackson, F. H., Basic integration; Quart. J. Math., 2(2), 1-16 (1951).
Kac, V. y P. Cheung, Quantum Calculus, Universitext, Springer, New York, USA (2002).
Kalia, R.N. (Ed), Recent Advances In Fractional Calculus, Global Publishing Company, East Lansing, USA (1993).
Kalla, S. L., Fractional integration operators involving generalized hypergeometric functions; Univ. Nac. Tucum´an, Rev. Matem´atica y F´ısica Te´orica, XX, 93-100 (1970).
Kalla, S. L. y R. Saxena, Integral operators involving hypergeometric functions II; Rev. Ser., 24, 31-36 (1974).
Kalla, S. L., Operators of fractional integration; Lecture Notes in Mathematics, 798, 258-280 (1980).
Kalla, S. L. y V. Kiryakova, An H-function generalized fractional calculus based upon composition of Erd´elyi-Kober operators in Lp; Math. Japon, 35, 1151-1171 (1990).
Kalla, S. L., L. Galu´e y H. M. Srivastava, Further results on an H-function generalized fractional calculus; Journal of Fractional Calculus, 4, 89-102 (1993).
Kalla, S. L. y L. Galu´e, Generalized fractional calculus based upon composition of some basic operators; in “Recent Advances In Fractional Calculus” Global Publishing Company, 145-178 (1993).
Kalla, S. L., R. K. Yadav y S. D. Purohit, On the Riemann-Liouville fractional q-integral operator involving a basic analogue of Fox H-function; Fractional Calculus & Applied Analysis, 8(3), 313-322 (2005).
Kalla, S. L. y Rao A., On Gru¨ss type inequality for a hypergeometric fractional integral; Le Matematiche, 66(1), 57-64 (2011).
Kilbas, A. A, Fractional calculus of the generalized Wright function; Fractional Calculus & Applied Analysis, 8(2), 113-126 (2005).
Kilbas, A. A, Fractional calculus of the generalized Wright function; Fractional Calculus & Applied Analysis, 8(2), 113-126 (2005).
Kilbas, A. A., H. M. Srivastava y J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Inc., New York, USA (2006)
Kilbas, A. A. y N. Sebastian, Fractional integration of the product of Bessel functions of the first kind; Fractional Calculus & Applied Analysis, 13(2), 159-175 (2010).
Kiryakova, V., Generalized Fractional Calculus and Applications, Logman Scientific and Technical, Harlow, England (1994).
Kober, H., On fractional integrals and derivatives; Quart. J. Math. Oxford Ser, 11, 193211 (1940).
Koelink, E., Quantum groups and q-special functions, Universiteit Van Amsterdam, Report 96-10 (1996).
Krug, A., Theorie der derivation; Akad. Wiss. Wien Denkenschriften Math., Naturwissen Kl., 57, 151-228 (1890).
Kuttner, B., Some theorems on fractional derivatives; Proc. London Math. Soc., 3(3), 480-497 (1953).
Lacriox, S. F., Trait´e du Calcul Diff´erentiel et du Calcul Integral, 3 ed., Courcier, Paris, France (1820).
Lagrange, J. L., Sur une nouvelle esp`ece de calcul relatif `a la differentiation et `a l’integration des quantit´es variables; Nouv. mem. Acad. Roy. Sci., reprinted in Oeuvres, Vol. 3 (1869), 441-476 (1772).
Leibniz, G. W., Letter from Hanover, Germany,1695 to L. A. L’Hospital, Leibnizen Mathematische Schriften, Vol. 2, 301-302. First published in 1849 (1962).
Leithold, L., El C´alculo con Geometr´ıa Ana´ıtica, 7 ed., Oxford University Press, Ciudad de Mexico, Mexico (1998).
Liouville, J., M´emoire: sur le calcul des diff´erentielles `a indices quelconques; J. de l’ˆEcole Polytechnique, 13, 71-162 (1832).
Luchko, Y. y J. J. Trujillo, Caputo type modification of the Erd´elyi-Kober fractional derivative; Frational Calculus & Applied Analysis, 10(3), 249-267 (2007).
Luchko, Y., Boundary value problems for the generalized time-fractional diffusion equation of distributed order; Fractional Calculus & Applied Analysis, 12(4), 409-422 (2009)
Luque, R. y L. Galu´e, Evaluation of fractional integrals involving Fox’s H-function; Rev. T´ec. Ing. Univ. Zulia, 21(1), 67-73 (1998).
Magin, R. L., Fractional Calculus and Bioengineering, Begell House Publishers Inc., New York, USA (2006).
Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, Singapore, Singapore (2010).
McBride, A. y G. Roach (Eds.), Fractional Calculus, Vol. 138, Research Notes in Mathematics, Pitman, Boston–London–Melbourne (1985).
Miller, K. S. y B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons Inc., New York, USA (1993)
Miller, A. R. y I. S. Moskowitz, Reduction of a class of Fox-Wright psi functions for certain rational parameters; Computers & Mathematics with Applications, 30(11), 73-82 (1995).
Mitrinovi´c, D. S., Analytic Inequalities, Springer-Verlag, New York, USA (1970).
Nishimoto, K., Fractional Calculus Vol. I, Descartes Press, Koriyama, Japan (1984).
Nishimoto, K., Fractional Calculus Vol. II, Descartes Press, Koriyama, Japan (1987).
Nishimoto, K., Fractional Calculus Vol. III, Descartes Press, Koriyama, Japan (1989).
Nishimoto, K. (Ed), Fractional Calculus and Its Applications, Nihon University, Koriyama, Japan (1990).
Nishimoto, K., Fractional Calculus Vol. IV, Descartes Press, Koriyama, Japan (1991).
¨Oˇgu¨nmez, H. y U. M. ¨Ozkan, Fractional quantum integral inequalities; J. of Inequal. and Appl., Vol. 2011, Article ID 787939, 7 pp. doi: 10.1155/2011/787939.
Oldham, K. B., A new approach to the solution of electrochemical problems involving difussion; Anal. Chem., 41, 1904 (1969).
Oldham, K. B., A unified treadment of electrolysis at an expanding mercury electrode; Anal. Chem., 41, 936 (1969).
Oldham, K. B. y J. Spanier, The replacement of Fick’s laws by a formulation involving semidifferentiation; J. Electroanal. Chem. Interfacial Electrochem., 26, 331-341 (1970).
Oldham, K. B. y J. Spanier, A general solution of the diffusion equation for semiinfinite geometries; J. Math. Anal. Appl., 39, 655-669 (1972).
Oldham, K. B., Diffusive transport to planar, cylindrical and speherical electrodes; J. Electroanal. Chem., 41, 351-360 (1973).
Oldham, K. B. y J. Spanier, The Fractional Calculus, Academic Press, New York, USA (1974).
Osler, T. J., Leibniz rule for fractional derivatives generalized and application to infinite series; SIAM J. Appl. Math., 18, 658-674 (1970).
Oustaloup, A., La D´erivation Non Enti`ere: Th´eorie, Synth`ese et Applications, Editions Herm`es, Paris, France (1995).
Owa, S., On certain generalization subclasses of analytic functions involving fractional calculus, in Frational Calculus and its Applications, Nihon University, Koriyama, Japan (1990).
Ozdemir, N., D. Avcı y B. B. Iskender The numerical solutions of a two-dimensional space-time Riesz-Caputo fractional diffusion equations; An International Journal of Optimization and Control: Theories & Applications, 1(1), 17-26 (2011).
Phillips, P. C. y S. J. Arnold, Visualizing Multivariate selection; Evolution, 43(6), 12091222 (1989).
Phillips, P. C., Time series regression with a unit root and infinite variance errors; Econometric Theory, 6, 44-62 (1990).
Pierantozzi, T., Estudio de las Generalizaciones Fraccionarias de las Ecuaciones Estandar de Difusi´on y de Ondas Universidad Complutense de Madrid, Departamento de Matem´atica Aplicada, Tesis doctoral, Madrid, Espan˜a (2006).
Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA (1999).
Post, E. L., Generalized differentiation; Trans. Amer. Math. Soc., 32, 723-781 (1930).
Prudnikov, A. P.,Yu. A. Brychkov y O. I. Marichev, Integrals and Series, Vol. 3, Gordon and Breach Science Publishers, New York, USA (1992).
Purohit, S. D. y R. K. Yadav, On generalized fractional q-integral operators envolving the q-Gauss hypergeometric function; Bull. Math. Anal. Appl., 2(4), 35-44 (2010).
Purohit, S. D. y S. L. Kalla, On fractional partial differential equations related to quantum mechanics; Journal of Physics A: Mathematical and Theoretical, 44, 1-8 (2011).
Purohit, S. D., E. U¸car y R. K. Yadav, On fractional integral inequalities and their qanalogues; Rev. Tecnociet´ıfica URU, 6, 53-66 (2014).
Purohit, S. D., E. U¸car y R. K. Yadav, On fractional integral inequalities and their qanalogues; Rev. Tecnociet´ıfica URU, 6, 53-66 (2014).
Rahimy, M., Applications of fractional differential equations; Applied Mathematical Sciences, 4(50), 2453-2461 (2010).
Rainville, E. D., Special functions, the MacMillan, New York, USA (1960).
Rajkovic, P. M. , S. D. Marinkovic y M. S. Stankovic, Fractional integrals and derivatives in q–calculus; Appl. Anal. Discrete Math., 1, 311-323 (2007).
Riemann, B., Versuch einer allgemeinen Auffasung der integration und differentiation, 2 ed., The Collected Works of Bernhard Riemman (H. Weber, ed.), New york, USA (1953).
Riesz, M., ‘L’int´egrale de Riemann-Liouville et le probl`eme de Cauchy; Acta Math., 81, 1-223 (1949).
Ritt, J. F., On a general class of linear homogeneous differential equations of infinite order with constant coefficients; Trans. Amer. Math. Soc., 18, 27-49 (1917).
Rogers, L. J., On a three-fold symmetry in the elements of Heine’s series; Proc. London Math. Soc., 24, 171-179 (1893).
Rogers, L. J., On the expansion of some infinite products; Proc. London Math. Soc., 24, 337-352 (1893).
Rogers, L. J., Second memoir on the expansion of certain infinite products; Proc. London Math. Soc., 318-343 (1894).
Rogers, L. J., Third memoir on the expansion of certain infinite products; Proc. London Math. Soc., 26, 15-32 (1895).
Rogers, L. J., On two theorems of combinatory analysis and some allied identities; Proc. London Math. Soc., 2(16), 315-336 (1917).
Rogers, L. J. y S. Ramanujan, Proof of certain identities in combinatory analysis (with a prefatory note by G. H. Hardy); Proc. Camb. Phil. Soc., 19, 211-216 (1919).
Ross, B. (Ed.), Fractional Calculus and Its Applications, Proceedings of the International Conference on Fractional Calculus and Its Applications, University of New Haven, West Haven, Conn., June 1974, Springer-Verlag, New York, USA (1975).
Ross, B., Fractional Calculus and its Application, Lecture Notes inMath. 457, SpringerVerlag, New York, USA (1975).
Ross, B., Fractional calculus: An histotical apologia for the development of a calculus using differentiation and antidifferentiation of non integral orders; Mathematics Magazine, 50(3), 115-122 (1977).
Saalschu¨tz, L., Eine Summationsformel; Zeitschr. Math. Phys., 35, 186-188 (1890).
Sabatier, J., O. P. Agrawal y J. A. Tenreiro, Advances in Fractional Calculus, Springer, New York, USA (2007).
Saigo, M., A remark on integral operators involving the Gauss hypergeo-metric function; Math. Reports College of Gen. Education, Kyuskyu Univ., 11, 135-143 (1978).
Saigo, M., On the H¨older continuity of the generalized fractional integrals and derivatives; Math. Rep. Kyushu Univ., 12(2), 55-62 (1980).
Salem, A., Some applications of fractional q-calculus and fractional q-Leibniz rule; Journal of Fractional Calculus and Applications, 2(4), 1-11 (2011).
Samko, S. G., A. A. Kilbas y O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk, Bielorusia (1987).
Samko, S. G., A. A. Kilbas y O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, Pennsylvania, USA (1993).
S´anchez, J. M., Historias de matem´aticas: g´enesis y desarrollo del c´alculo fraccional; Pensamiento Matem´atico, 1, 1-15 (2011).
Saxena, R. K., On fractional integration operators; Math. Z., 96, 289-291 (1967).
Saxena, R. K., G. C. Modi y S. L. Kalla, A basic analogue of Fox’s H-function; Rev. T´ec. Ing. Univ. Zulia, 6, 139-143 (1983).
Saxena, R. K. y R. Kumar, Recurrence relations for the basic analogue of the H-function; J. Nat. Acad. Math. 8, 48-54 (1990).
Saxena, R. K., R. K. Yadav y otros dos, Kober fractional q-integral operator of the basic analogue of the H-function; Rev. T´ec. Ing. Univ. Zulia, 28(2) 154-158 (2005).
Saxena, R. K., Ravi Saxena y S. L. Kalla, Solution of space-time fractional Schrodinger equation occurring in quantum m
Scott Blair, G. W., B. C. Veinoglou y J. E. Caffyn, Limitations of the newtonian time scale in relation to non-equilibrium rheological states and a theory of quasi-properties; Proc. Roy. Soc., 189(1016), 69-87 (1947).
Scott Blair, G. W., The role of psychophysics in rheology; J. Colloid Sci., 2, 21-32 (1947).
Scott Blair, G. W y J. E. Caffyn, An application of the theory of quasiproperties to the treatment of anomalous stress-strain relations; Philos. Mag., 40, 80-94 (1949).
Scott Blair, G. W., Measurements of Mind and Matter, Dennis Dobson, London, England (1950).
Scott Blair, G. W., Some aspects of the search for invariants; British J. Philos. Sci., 1(3), 230-244 (1950).
Sears, D. B., Two identities of Bailey; J. London Math. Soc., 27, 510-511 (1952).
Secer, A., S. D. Purohit y otros dos, A generalized q-Gru¨ss inequality involving the Riemann-Liouville fractional q-integrals; Journal of Applied Mathematics,Hindawi Publishin Corporation, Vol. 2014, article ID 914320, http://dx.doi.org/10.1155/2014/914320.
Shermergor, T. D., On the use of fractional differentiation operators for the description of elastic-after effect properties of materials; J. Appl. Mech. Tech. Phys, 7(6), 85-87 (1966).
Singh, Y. y H. K. Mandia, On some Kober fractional q-integral operator of the basic analogue of the H-function; International Journal of Theoretical and Applied Physics, 1(I), 53-62 (2011).
Slater, L. J., A new proof of Roger‘s transformations of infinite series; Proc. London Math. Soc., 2(53), 460-475 (1951).
Slater, L. J., Integrals representing general hypergeometric transformations; Quart. J. Math., 2(3), 206-216 (1952).
Slater, L. J., Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, England (1966).
Somorjai, R. L. y D. M. Bishop, Integral transformation trial functions of the fractional integral class; Phys. Rev., A1, 1013-1026 (1970).
Sonine, N.Ya., Report on differentiation with an arbitrary index; (Ru-ssian), Proc. Second Congress of Russian Naturalists, 2, 18-21 (1870).
Srivastava, H. M. y P. W. Karlsson, Multiple Gaussian Hypergeometric Series, John Wiley & Sons, New York, USA (1985).
Srivastava H. M. y A. K. Agarwal, Generating functions for a class of q-polynomials; Annali di Matematica Pura ed Applicata, IV(154), 99-109 (1989).
Sulaiman, W. T., On some new fractional q-integral inequalities; South Asian J. of Math., 2(5), 450-459 (2012).
Tarasov, V. E., Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, New York, USA (2011).
Thomae, J., Beitr¨age zur Theorie der durch die Heinesche Reihe: 1 + [(1−qα) 1−qβ ]/[(1−q)(1−qγ)] x + ... darstellbaren Functionen; J. reine angew. Math. 70, 258-281 (1869).
Vinagre, B. M. y C. A. Monje, Introducci´on al control fraccionario; Rev. Iberoam. de Autom´at. e Inform. Indust., 3(3), 5-23 (2006).
Weber y H. Dover (Eds.), Versuch einer allgemeinen auffasung der integration und differentiation, The collected works of Bernhard Riemann, New York, USA (1953).
Wei, Z., W. Dong y J. Che, Periodic boundary value problems for fractional differential equations involving a Riemann Liouville fractional derivative; Nonlinear Analysis, 73, 3232-3238 (2010).
West, B. J., M. Bologna y P. Grigolini, Physics of Fractal Operators, Springer, New York, USA (2003).
Weyl, H., Bemerkungen zum begriff des differentialquotienten gebrochener ordnung; Vierteljschr. Naturforsch. Gesellsch. Zu¨rich, 62, 296-302 (1917).
Whipple, F. J. W., On well-poised series, generalized hypergeometric series having parameters in pairs, each pair with the same sum; Proc. London math. Soc., 2(24), 247-263 (1926).
Whipple, F. J. W., Well-poised series, and other generalized hypergeometric series; Proc. London math. Soc., 2(25), 525-544 (1926).
Whipple, F. J. W., Algebraic proofs of the theorems of Cayley and Orr concerning the products of certain hypergeometric series; J. London Math. Soc., 2, 85-90 (1927).
Whipple, F. J. W., On a formula implied in Orr’s theorems concerning the product of hypergeometric series; J. London Math., Soc., 4, 48-50 (1929).
Wiener, N., The operational calculus; Math. Ann., 95, 557-584 (1926).
Yadav, R. K. y S. D. Purohit, Application of Riemann-Liouville fractional q-integral operator to basic hypergeometric functions; Acta Ciencia Indica, 30(iii), 593-600 (2004).
Yadav, R. K. y S. D. Purohit, On applications of Kober fractional q-integral operator to certain basic hypergeometric functions; J. Rajasthan Acad. Phy. Sci. 5(4), 437-448 (2006).
Yadav, R. K. y S. D. Purohit, On applications of Weyl fractional q-integral operator to generalized basic hypergeometric functions; Kyungpook Math. J., 46, 235-245 (2006).
Yadav, R. K., S. D. Purohit y S. L. Kalla, On generalized Wely fractional q-integral operator involving generalized basic hypergeometric functions; Fractional Calculus & Applied Analysis, 11(2), 129-142 (2008).
Yadav, R. K., S. L. Kalla y G. Kaur, On fractional q-integral operator involving the basic multiple hypergeometric functions; Algebras Groups and Geometries, 27(1), 97-116 (2010).
Zhu, C., W. Yang y O. Zhao, Some new fractional q-integral Gru¨ss-type inequalities and other inequalities; J. of Inequal. and Appl., Vol. 2012, article 299, 2012, DOI: 10.1186/1029-242X-2012-299.
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spelling Castillo Pérez, Jaime2023-07-27T20:51:45Z2023-07-27T20:51:45Z20209789585178199https://repositoryinst.uniguajira.edu.co/handle/uniguajira/741Este libro contiene elementos importantes tanto del cálculo fraccional como del q-fraccional. Está diseñado para profesionales en Matemáticas, Física y ciencias de Ingenierías que deseen tener una primera aproximación a estas teorías. Su contenido está distribuido de la siguiente manera: En el primer capítulo se presentan algunos elementos de cálculo fraccional, inicialmente se hace un recorrido sobre el desarrollo histórico del mismo, desde sus inicios hacia el siglo XVII hasta la fecha. Se presentan algunas definiciones y se muestran los operadores más usuales de dicho cálculo. En el segundo capítulo se presentan las funciones más usadas en el cálculo fraccional, entre las que se cuentan a la función gamma, función gamma incompleta, función beta, función hipergeométrica generalizada, función hipergeométrica de Fox-Wright, función H, funciones de Mittag-Leffler, función de Agarwal, función de Erd`elyi, función de Robotnov-Hartley, funciónde Miller-Ross, funciones generalizadas de seno y coseno, funciones de Bessel. Se muestran algunas aplicaciones del operador derivada fraccional de Riemann-Liouville a una variedad de funciones. En el tercer capítulo se presentan los operadores de integración fraccional establecidos por varios investigadores en este campo y se muestran algunas aplicaciones. Introducción al cálculo fraccional y q-fraccional2 En el cuarto capítulo se hace una breve reseña histórica del cálculo q-fraccional, se define la q-derivada, la q-integral y varios conceptos que soportan el desarrollo de este campo de la matemática. En el quinto capítulo se presentan las funciones usadas en el cálculo q-fraccional, las cuales se establecen como análogas básicas de las funciones factorial, gamma, beta, hipergeométrica, exponencial, Bessel, H, Wright. Se introduce un nuevo teorema donde se establece la convergencia absoluta para la análoga básica de la función hipergeométrica de Fox-Wright. En el sexto capítulo se presentan los operadores q-fraccionales con sus reglas de composición y ciertas aplicaciones a las q-funciones79 páginasapplication/pdfspaUniversidad de La GuajiraUniversidad de La GuajiraCopyright - Universidad de La Guajira, 2020info:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)http://purl.org/coar/access_right/c_abf2Introducción al cálculo fraccional y q-fraccional : con aplicacionesLibrohttp://purl.org/coar/resource_type/c_2f33Textinfo:eu-repo/semantics/bookhttps://purl.org/redcol/resource_type/LIBinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Abel, N.H., Resolution d’un probl`eme de mecanique; Oeuvres Compl`etes, 1, 27-30 (1823).Abel, N.H., Sur quelques int´egrales d´efinies; Oeuvres Compl`etes, 1, 93-102 (1825).Agarwal, R. P., A q-analogue of MacRobert’s generalized E-function; Ganita, 11, 49-63 (1960).Agarwal, R. P., Generalized Hypergeometric Series, Asia Publishing House, Bombay, New York,USA, (1963).Agarwal, R. P., Certain fractional q-integrals and q-derivatives; Proc. Camb. Phil. Soc., 66, 365-370 (1969).Agarwal, R. P.; M. Benchohra y S. Hamani, Boundary value problems for fractional differential equations; Georgian Mathematical Journal, 16(3), 401-411 (2009).Al-Salam, W. A., q-Analogues of Cauchy’s formula; Proc. Am. Math. Soc., 17, 182-184 (1952-1953).Al-Salam, W. A., Some fractional q-integrals and q-derivatives; Proc. Edin. Math. Soc., 2(15), 135-140 (1966).Anastassiou, G. A., Fractional Differentiation Inequalities, Springer, New York, USA, (2009).Anastassiou, G. A., Advances on Fractional Inequalities, Springer, New York, USA, (2011).Andrews, G. E., A simple proof of Jacobi’s triple product identity; Proc. Amer. Math. Soc., 16, 333-334 (1965).Andrews, G. E., On basic hypergeometric series, mock theta functions, and partitions I; Quart. J. Math., 2(17), 64-80 (1966).Andrews, G. E., On basic hypergeometric series, mock theta functions, and partitions II; Quart. J. Math., 2(17), 132-143 (1966).] Andrews, G. E., q-identities of Auluck, Carlitz, and Rogers; Duke Math. J., 33, 575-581 (1966).Andrews, G. E., On q-difference equations for certain well-poised basic hypergeometric series; Quart. J. Math., 2(19), 433-447 (1968).Andrews, G. E., On Ramanujan’s summation of 1ψ1 (a;b;z); Proc. Amer. Math. Soc., 22, 552-553 (1969).Annaby, M. H. y Z. S. Mansour, q-Fractional Calculus and Equations, Springer, New York, USA, (2012).Bagley, R. L. y P. J. Torvik, On the fractional calculus model of viscoelastic behaviour; J. Rheol., 30(1), 133 -155 (1986).Bagley, R. L., On the fractional order initial value problem and its engineering applications; In Frational Calculus and Its Applications, Koriyama, Japan, Nihon University, pp 11-20 (1990).Belarbi, S. y Z. Dahmani, On some new fractional integral inequalities; Int. Journal of Math. Analysis, 4(4), 185-191 (2010).Belavin, V. A.; R. Sh. Nigmatullin y otros dos autores, Fractional differentiation of oscillographic polarograms by means of an electrochemical two-terminal network; Trudy Kazan. Aviation. Inst., 5, 144-152 (1964).Boole, G., On a general method in analysis; Philos. Trans. Roy. Soc., 134, 225-282 (1844).Bourlet, M. C., Sur les op´erations en g´en´eral et les ´equations diff´erentielles lin´eaires d’ordre infini; Annales scientifiques de l’´E.N.S., 3(14), 133-190 (1897).Caputo, M., Linear models of dissipation whose Q is almost frequency independent II; Geophis, J. R. Astr. Soc., 13, 529 - 539 (1967).Caputo, M., Elasticit´a e Dissipazione, Zanichelli Publisher, Bologna, Italy (1969).Carlitz, L., Some polynomials related to theta functions; Annali di Matematica pura ed Applicata, 4(41), 359-373 (1955).Carlitz, L., A q-analogue of a formula of Toscano; Boll. Unione Math. Ital., 12, 414-417 (1957).Carpinteri, A. y F. Mainardi (Eds.), Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics, Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien, Austria (1997).Carson, J. R., The Heaviside operational calculus; Bull. Amer. Math. Soc., 32(1), 43-68 (1926).Cauchy, A. L., M´emoire sur les fonctions dont plusieurs valeurs sont li´ees entre elles par une ´equation lin´eaire, et sur diverses transformations de produits compos´es d’un nombre ind´efini de facteurs; C. R. Acad. Sci. Paris, T. XVII, p. 523, Oeuvres de Cauchy, 1re s´erie, T. VIII, Gauthier-Villars, 42-50 (1843, 1893).Choi, J.; D. Ritelli y P. Agarwal, Some new inequalities involving Generalized Erd´erlyiKober fractional q-integral operator; Appl. Math. Sci., 9(72), 3577-3591 (2015).Dahmani, Z.; L. Tabharit y S. Taf, New generalisations of Gru¨ss inequality using RiemannLiouville fractional integrals; Bulletin of Math. Anal. and Applic., 2(3), 93-99 (2010).Dahmani, Z. y A. Benzidane, New weighted Gru¨ss type inequalities via (α,β) fractional q-integral inequalities; International Journal of Innovation and Applied Studies, 1(1), 76-83 (2012).Dalir, M. y M. Bashour, Applications of fractional calculus; Applied Mathematical Sciences, 4(21), 1021-1032 (2010).Das, S., Functional Fractional Calculus, 2 ed., Springer-Verlag Berlin Heidelberg, New York, USA (2011).Davis, H. D., The Theory of Linear Operators, Principia Press, Bloomington Indiana, USA (1936).Delgado, M. y L. Galu´e, Fractional q-integral operator involving basic hypergeometric function; Algebras Groups Geom., 25, 53-74 (2008).Diethelm, K., The Analysis of Fractional Differential Equations, Springer, New York, USA (2010).Dixon, A. C., Summation of a certain series; Proc. London math. Soc., 1(35), 285-289 (1903).Dougall, J., On Vandermonde’s theorem and some more general expansions; Proc. Edin. math. Soc., 25, 114-132 (1907).Dragomir, S. S., A generalization of Gru¨ss inequality in inner product spaces and applications; Journal of Math. Anal. and Applic., 237(1), 74-82 (1999).Dragomir, S. S., A Gru¨ss type inequality for sequences of vectores in inner product spaces and applications; Journal of Inequalities in Pure and Applied Math., 1(2), 1-11 (2000).Dragomir, S. S., Some integral inequalities of Gru¨ss type; Indian Journal of Pure and Applied Mathematics, 31(4), 397-415 (2000).Erd´elyi, A., Transformation of hypergeometric integrals by means of fractional integration by parts; Quart. J. Math. (Oxford), 10, 176-189 (1939).Erd´elyi, A., On fractional integration and its applications to the theory of Hankel transform; Quart. J. Math. (Oxford), 11(1), 293-303 (1940).Erd´elyi, A.; W. Magnus y otros dos, Tables of Integral Transforms Vol. II, McGraw-Hill, New York, USA (1954).Erd´elyi, A., An integral equation involving Legendre functions; SIAM J. Appl. Math., 12, 15-30 (1964).Erd´elyi, A., Axially symmetric potentials and fractional integration; J. Appl. Math., 13(1), 216-228 (1965).Ernst, T., The History of q-Calculus and a new Method (Licentiate Thesis), Department of Mathematics of Uppsala University, Uppsala, Suecia (2002).Euler, L., M´emoire dans le tome V des Comment, Saint Petersberg Ann´ees, 55 (1730).Galu´e, L. y S. L. Kalla, Operadores integrales que involucran funciones cil´ındricas incompletas; Rev. T´ec. Ing. Univ. Zulia, 11(2), 111-119 (1988).Galu´e, L., Generalized Erd´erlyi-Kober fractional q-integral operator; Kuwait J. Sci. Eng., 36(2A), 21-34 (2009).Galu´e, L., Generalized Weyl fractional q-integral operator; Algebras Groups and Geometries, 26, 163-178 (2009).Galu´e, L., On composition of fractional q−integral operators involving basic hipergeometric functions; Journal of Inequalities and Special Functions, 1(1), 39-52 (2010).Galu´e, L., Unification of q-fractional integral operator; Algebras Groups and Geom., 28, 283-298 (2011).Galu´e, L., Unified fractional q-integral operator of q-special functions; Algebras Groups and Geom., 28, 185-204 (2011).Galu´e, L., Some results on a fractional q-integral operator involving generalized basic hypergeometric function; Rev. T´ec. Ing. Univ. Zulia, 35(3), 302 -310 (2012).Galu´e, L., Some results involving generalized Erd´erlyi-Kober fractional q-integral operator; Rev. Tecnociet´ıfica URU, 6, 77-89 (2014).Garg, M. y L.Chanchlani, q-Analogues of Saigo’s fractional calculus operators; Bulletin of Mathematical Analysis and Applications, 3(4), 169-179 (2011).Garg, M. y L. Chanchlani, Kober fractional q-derivative operators; Le Matematiche, 66(1), 13-26 (2011).Gasper, G. y M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, New York, USA (2004).Gauchman, H., integral inequalities in q-calculus; Computers and Mathematics with Applications, 47(2-3), 281-300 (2004).Gauss, C. F., Disquisitiones generales circa seriem infinitam 1+ αβ γ·1 +...; Comm. soc. reg. sci. G¨ott. rec., Vol. II. Reprinted in Werke, 3 123-162 (1813, 1876).Gemant, A., A method of analyzing experimental results obtained from elastoviscous bodies; Physics, 7, 311-317 (1936).Graham, A.; G. W. Scott Blair y R. F. J. Whiters, A methodological problem in rheology; British J. Philos. Sci., 11(44), 265-278 (1961).Grenness, M. y K. B. Oldham, Semiintegral electroanalysis: theory and verification; Ana. Chem., 44, 1121-1139 (1972).Gru¨nwald, A. K., Uber begrenzte derivationen und deren anwendung; Z. Angew. Math. Phys., 12, 441-480 (1867).Gru¨ss, D., ¨Uber das maximum des absoluten Betrages von 1 (b−a) b a f (x)g (x)dx − 1 (b−a)2 b a f (x)dx b a g (x)dx; Math. Z. 39, 215-226 (1935).Gupta, K. y A. Gupta, Study of modified ¯ H−Transform and generalized fractional integral operator of Weyl type; Int. J. Pure Appl. Sci. Technol., 7(1), 59-67 (2011).Hahn, W., ¨Uber die h¨oheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen; Math. Nachr., 3, 257-294 (1950).Hahn, W., ¨Uber uneigentliche L¨osungen linearer geometrischer differenzengleichungen; Math. Annalen, 125, 67-81 (1952).Hahn, W., Die mechanische Deutung einer geometrischen Differenzengleichung; Zeitschr. angew. Math. Mech., 33, 270-272 (1953).Hardy, G. H., Notes on some points in the integral calculus; Messenger of Math., 47, 145-150 (1917).Hardy, G. H. y J. E. Littlewood, Some properties of fractional integrals; Proc. London Math. Soc., 2(24), 37-41 (1925).Hardy, G. H. y J. E. Littlewood, Some properties of fractional integrals I; Math. Z., 27, 565-606 (1928).Hardy, G. H. y J. E. Littlewood, Some properties of fractional integrals II; Math. Z., 34, 403-439 (1932).Heaviside, O., Electrical papers, Macmillan, London, England (1892).Heaviside, O., On operators in physical mathematics; Proc. Roy. Soc., 504-529 (1893).Heaviside, O., Electromagnetic Theory, Vol. I, The electrician printing and publishing company, Ltd., London, England (1893).Heaviside, O., On operators in physical mathematics; Proc. Roy. Soc., 54, 105-143 (1894).Heaviside, O., Electromagnetic Theory, Vol. II, The electrician printing and publishing company, Ltd., London, England (1920).Heine, E., ¨Uber die Reihe 1 + [(1−qα) 1−qβ ]/[(1−q)(1−qγ)] x + [(1−qα)(1−qα+1) 1−qβ 1−qβ+1 ]/[(1−Heine, E., Untersuchungen u¨ber die Reihe 1 + [(1−qα) 1−qβ ]/[(1−q)(1−qγ)] x+ [(1−qα)(1−qα+1) 1−qβ 1−qβ+1 ]/ [(1−q)(1−q2)(1−qγ)(1−qγ+1)]}x2 + ...; J. reine angew. Math. 34, 285-328 (1847).Heine, E., Handbuch der Kugelfunctionen, Theorie und Anwendungen, vol. 1, Berlin, Germany (1878).Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific publishing, New Jersey, USA (2000).Higgins, T. P., The Use of Fractional Integral Operators for Solving Nonhomogeneous Differential Equations, Document DI-82-0677, Boeing Sci. Res. Lab., Washington, USA (1967).Holmgren, H. J., Om differentialkalkylen med indices of hvad nature sam helst Kongliga svenska; Vetenskaps-akademiens handlinger, 5(11), 1-83 (1864).Isogawa S., N. Kobachi y S. Hamada, A q-analogue of Riemann-Liouville fractional derivative; Res. Rep. Yatsushiro Nat. Coll. Tech., 29, 59-68 (2007).Jackson, F. H., A generalization of the functions Γ(n) and xn; Proc. Roy. Soc., 74, 64-72 (1904).Jackson, F. H., The application of basic numbers to Bessel’s and Legendre’s functions; Proc. Lond. Math. Soc., 32, 1–23 (1905).Jackson, F. H., On q-functions and a certain difference operator; Trans. Roy. Soc. Edin., 46, 253-281 (1908).Jackson, F. H., On q-definite integrals; Quart. J. Pure and Appl. Math., 41, 193-203 (1910).Jackson, F. H., Basic integration; Quart. J. Math., 2(2), 1-16 (1951).Kac, V. y P. Cheung, Quantum Calculus, Universitext, Springer, New York, USA (2002).Kalia, R.N. (Ed), Recent Advances In Fractional Calculus, Global Publishing Company, East Lansing, USA (1993).Kalla, S. L., Fractional integration operators involving generalized hypergeometric functions; Univ. Nac. Tucum´an, Rev. Matem´atica y F´ısica Te´orica, XX, 93-100 (1970).Kalla, S. L. y R. Saxena, Integral operators involving hypergeometric functions II; Rev. Ser., 24, 31-36 (1974).Kalla, S. L., Operators of fractional integration; Lecture Notes in Mathematics, 798, 258-280 (1980).Kalla, S. L. y V. Kiryakova, An H-function generalized fractional calculus based upon composition of Erd´elyi-Kober operators in Lp; Math. Japon, 35, 1151-1171 (1990).Kalla, S. L., L. Galu´e y H. M. Srivastava, Further results on an H-function generalized fractional calculus; Journal of Fractional Calculus, 4, 89-102 (1993).Kalla, S. L. y L. Galu´e, Generalized fractional calculus based upon composition of some basic operators; in “Recent Advances In Fractional Calculus” Global Publishing Company, 145-178 (1993).Kalla, S. L., R. K. Yadav y S. D. Purohit, On the Riemann-Liouville fractional q-integral operator involving a basic analogue of Fox H-function; Fractional Calculus & Applied Analysis, 8(3), 313-322 (2005).Kalla, S. L. y Rao A., On Gru¨ss type inequality for a hypergeometric fractional integral; Le Matematiche, 66(1), 57-64 (2011).Kilbas, A. A, Fractional calculus of the generalized Wright function; Fractional Calculus & Applied Analysis, 8(2), 113-126 (2005).Kilbas, A. A, Fractional calculus of the generalized Wright function; Fractional Calculus & Applied Analysis, 8(2), 113-126 (2005).Kilbas, A. A., H. M. Srivastava y J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Inc., New York, USA (2006)Kilbas, A. A. y N. Sebastian, Fractional integration of the product of Bessel functions of the first kind; Fractional Calculus & Applied Analysis, 13(2), 159-175 (2010).Kiryakova, V., Generalized Fractional Calculus and Applications, Logman Scientific and Technical, Harlow, England (1994).Kober, H., On fractional integrals and derivatives; Quart. J. Math. Oxford Ser, 11, 193211 (1940).Koelink, E., Quantum groups and q-special functions, Universiteit Van Amsterdam, Report 96-10 (1996).Krug, A., Theorie der derivation; Akad. Wiss. Wien Denkenschriften Math., Naturwissen Kl., 57, 151-228 (1890).Kuttner, B., Some theorems on fractional derivatives; Proc. London Math. Soc., 3(3), 480-497 (1953).Lacriox, S. F., Trait´e du Calcul Diff´erentiel et du Calcul Integral, 3 ed., Courcier, Paris, France (1820).Lagrange, J. L., Sur une nouvelle esp`ece de calcul relatif `a la differentiation et `a l’integration des quantit´es variables; Nouv. mem. Acad. Roy. Sci., reprinted in Oeuvres, Vol. 3 (1869), 441-476 (1772).Leibniz, G. W., Letter from Hanover, Germany,1695 to L. A. L’Hospital, Leibnizen Mathematische Schriften, Vol. 2, 301-302. First published in 1849 (1962).Leithold, L., El C´alculo con Geometr´ıa Ana´ıtica, 7 ed., Oxford University Press, Ciudad de Mexico, Mexico (1998).Liouville, J., M´emoire: sur le calcul des diff´erentielles `a indices quelconques; J. de l’ˆEcole Polytechnique, 13, 71-162 (1832).Luchko, Y. y J. J. Trujillo, Caputo type modification of the Erd´elyi-Kober fractional derivative; Frational Calculus & Applied Analysis, 10(3), 249-267 (2007).Luchko, Y., Boundary value problems for the generalized time-fractional diffusion equation of distributed order; Fractional Calculus & Applied Analysis, 12(4), 409-422 (2009)Luque, R. y L. Galu´e, Evaluation of fractional integrals involving Fox’s H-function; Rev. T´ec. Ing. Univ. Zulia, 21(1), 67-73 (1998).Magin, R. L., Fractional Calculus and Bioengineering, Begell House Publishers Inc., New York, USA (2006).Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, Singapore, Singapore (2010).McBride, A. y G. Roach (Eds.), Fractional Calculus, Vol. 138, Research Notes in Mathematics, Pitman, Boston–London–Melbourne (1985).Miller, K. S. y B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons Inc., New York, USA (1993)Miller, A. R. y I. S. Moskowitz, Reduction of a class of Fox-Wright psi functions for certain rational parameters; Computers & Mathematics with Applications, 30(11), 73-82 (1995).Mitrinovi´c, D. S., Analytic Inequalities, Springer-Verlag, New York, USA (1970).Nishimoto, K., Fractional Calculus Vol. I, Descartes Press, Koriyama, Japan (1984).Nishimoto, K., Fractional Calculus Vol. II, Descartes Press, Koriyama, Japan (1987).Nishimoto, K., Fractional Calculus Vol. III, Descartes Press, Koriyama, Japan (1989).Nishimoto, K. (Ed), Fractional Calculus and Its Applications, Nihon University, Koriyama, Japan (1990).Nishimoto, K., Fractional Calculus Vol. IV, Descartes Press, Koriyama, Japan (1991).¨Oˇgu¨nmez, H. y U. M. ¨Ozkan, Fractional quantum integral inequalities; J. of Inequal. and Appl., Vol. 2011, Article ID 787939, 7 pp. doi: 10.1155/2011/787939.Oldham, K. B., A new approach to the solution of electrochemical problems involving difussion; Anal. Chem., 41, 1904 (1969).Oldham, K. B., A unified treadment of electrolysis at an expanding mercury electrode; Anal. Chem., 41, 936 (1969).Oldham, K. B. y J. Spanier, The replacement of Fick’s laws by a formulation involving semidifferentiation; J. Electroanal. Chem. Interfacial Electrochem., 26, 331-341 (1970).Oldham, K. B. y J. Spanier, A general solution of the diffusion equation for semiinfinite geometries; J. Math. Anal. Appl., 39, 655-669 (1972).Oldham, K. B., Diffusive transport to planar, cylindrical and speherical electrodes; J. Electroanal. Chem., 41, 351-360 (1973).Oldham, K. B. y J. Spanier, The Fractional Calculus, Academic Press, New York, USA (1974).Osler, T. J., Leibniz rule for fractional derivatives generalized and application to infinite series; SIAM J. Appl. Math., 18, 658-674 (1970).Oustaloup, A., La D´erivation Non Enti`ere: Th´eorie, Synth`ese et Applications, Editions Herm`es, Paris, France (1995).Owa, S., On certain generalization subclasses of analytic functions involving fractional calculus, in Frational Calculus and its Applications, Nihon University, Koriyama, Japan (1990).Ozdemir, N., D. Avcı y B. B. Iskender The numerical solutions of a two-dimensional space-time Riesz-Caputo fractional diffusion equations; An International Journal of Optimization and Control: Theories & Applications, 1(1), 17-26 (2011).Phillips, P. C. y S. J. Arnold, Visualizing Multivariate selection; Evolution, 43(6), 12091222 (1989).Phillips, P. C., Time series regression with a unit root and infinite variance errors; Econometric Theory, 6, 44-62 (1990).Pierantozzi, T., Estudio de las Generalizaciones Fraccionarias de las Ecuaciones Estandar de Difusi´on y de Ondas Universidad Complutense de Madrid, Departamento de Matem´atica Aplicada, Tesis doctoral, Madrid, Espan˜a (2006).Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA (1999).Post, E. L., Generalized differentiation; Trans. Amer. Math. Soc., 32, 723-781 (1930).Prudnikov, A. P.,Yu. A. Brychkov y O. I. Marichev, Integrals and Series, Vol. 3, Gordon and Breach Science Publishers, New York, USA (1992).Purohit, S. D. y R. K. Yadav, On generalized fractional q-integral operators envolving the q-Gauss hypergeometric function; Bull. Math. Anal. Appl., 2(4), 35-44 (2010).Purohit, S. D. y S. L. Kalla, On fractional partial differential equations related to quantum mechanics; Journal of Physics A: Mathematical and Theoretical, 44, 1-8 (2011).Purohit, S. D., E. U¸car y R. K. Yadav, On fractional integral inequalities and their qanalogues; Rev. Tecnociet´ıfica URU, 6, 53-66 (2014).Purohit, S. D., E. U¸car y R. K. Yadav, On fractional integral inequalities and their qanalogues; Rev. Tecnociet´ıfica URU, 6, 53-66 (2014).Rahimy, M., Applications of fractional differential equations; Applied Mathematical Sciences, 4(50), 2453-2461 (2010).Rainville, E. D., Special functions, the MacMillan, New York, USA (1960).Rajkovic, P. M. , S. D. Marinkovic y M. S. Stankovic, Fractional integrals and derivatives in q–calculus; Appl. Anal. Discrete Math., 1, 311-323 (2007).Riemann, B., Versuch einer allgemeinen Auffasung der integration und differentiation, 2 ed., The Collected Works of Bernhard Riemman (H. Weber, ed.), New york, USA (1953).Riesz, M., ‘L’int´egrale de Riemann-Liouville et le probl`eme de Cauchy; Acta Math., 81, 1-223 (1949).Ritt, J. F., On a general class of linear homogeneous differential equations of infinite order with constant coefficients; Trans. Amer. Math. Soc., 18, 27-49 (1917).Rogers, L. J., On a three-fold symmetry in the elements of Heine’s series; Proc. London Math. Soc., 24, 171-179 (1893).Rogers, L. J., On the expansion of some infinite products; Proc. London Math. Soc., 24, 337-352 (1893).Rogers, L. J., Second memoir on the expansion of certain infinite products; Proc. London Math. Soc., 318-343 (1894).Rogers, L. J., Third memoir on the expansion of certain infinite products; Proc. London Math. Soc., 26, 15-32 (1895).Rogers, L. J., On two theorems of combinatory analysis and some allied identities; Proc. London Math. Soc., 2(16), 315-336 (1917).Rogers, L. J. y S. Ramanujan, Proof of certain identities in combinatory analysis (with a prefatory note by G. H. Hardy); Proc. Camb. Phil. Soc., 19, 211-216 (1919).Ross, B. (Ed.), Fractional Calculus and Its Applications, Proceedings of the International Conference on Fractional Calculus and Its Applications, University of New Haven, West Haven, Conn., June 1974, Springer-Verlag, New York, USA (1975).Ross, B., Fractional Calculus and its Application, Lecture Notes inMath. 457, SpringerVerlag, New York, USA (1975).Ross, B., Fractional calculus: An histotical apologia for the development of a calculus using differentiation and antidifferentiation of non integral orders; Mathematics Magazine, 50(3), 115-122 (1977).Saalschu¨tz, L., Eine Summationsformel; Zeitschr. Math. Phys., 35, 186-188 (1890).Sabatier, J., O. P. Agrawal y J. A. Tenreiro, Advances in Fractional Calculus, Springer, New York, USA (2007).Saigo, M., A remark on integral operators involving the Gauss hypergeo-metric function; Math. Reports College of Gen. Education, Kyuskyu Univ., 11, 135-143 (1978).Saigo, M., On the H¨older continuity of the generalized fractional integrals and derivatives; Math. Rep. Kyushu Univ., 12(2), 55-62 (1980).Salem, A., Some applications of fractional q-calculus and fractional q-Leibniz rule; Journal of Fractional Calculus and Applications, 2(4), 1-11 (2011).Samko, S. G., A. A. Kilbas y O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk, Bielorusia (1987).Samko, S. G., A. A. Kilbas y O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, Pennsylvania, USA (1993).S´anchez, J. M., Historias de matem´aticas: g´enesis y desarrollo del c´alculo fraccional; Pensamiento Matem´atico, 1, 1-15 (2011).Saxena, R. K., On fractional integration operators; Math. Z., 96, 289-291 (1967).Saxena, R. K., G. C. Modi y S. L. Kalla, A basic analogue of Fox’s H-function; Rev. T´ec. Ing. Univ. Zulia, 6, 139-143 (1983).Saxena, R. K. y R. Kumar, Recurrence relations for the basic analogue of the H-function; J. Nat. Acad. Math. 8, 48-54 (1990).Saxena, R. K., R. K. Yadav y otros dos, Kober fractional q-integral operator of the basic analogue of the H-function; Rev. T´ec. Ing. Univ. Zulia, 28(2) 154-158 (2005).Saxena, R. K., Ravi Saxena y S. L. Kalla, Solution of space-time fractional Schrodinger equation occurring in quantum mScott Blair, G. W., B. C. Veinoglou y J. E. Caffyn, Limitations of the newtonian time scale in relation to non-equilibrium rheological states and a theory of quasi-properties; Proc. Roy. Soc., 189(1016), 69-87 (1947).Scott Blair, G. W., The role of psychophysics in rheology; J. Colloid Sci., 2, 21-32 (1947).Scott Blair, G. W y J. E. Caffyn, An application of the theory of quasiproperties to the treatment of anomalous stress-strain relations; Philos. Mag., 40, 80-94 (1949).Scott Blair, G. W., Measurements of Mind and Matter, Dennis Dobson, London, England (1950).Scott Blair, G. W., Some aspects of the search for invariants; British J. Philos. Sci., 1(3), 230-244 (1950).Sears, D. B., Two identities of Bailey; J. London Math. Soc., 27, 510-511 (1952).Secer, A., S. D. Purohit y otros dos, A generalized q-Gru¨ss inequality involving the Riemann-Liouville fractional q-integrals; Journal of Applied Mathematics,Hindawi Publishin Corporation, Vol. 2014, article ID 914320, http://dx.doi.org/10.1155/2014/914320.Shermergor, T. D., On the use of fractional differentiation operators for the description of elastic-after effect properties of materials; J. Appl. Mech. Tech. Phys, 7(6), 85-87 (1966).Singh, Y. y H. K. Mandia, On some Kober fractional q-integral operator of the basic analogue of the H-function; International Journal of Theoretical and Applied Physics, 1(I), 53-62 (2011).Slater, L. J., A new proof of Roger‘s transformations of infinite series; Proc. London Math. Soc., 2(53), 460-475 (1951).Slater, L. J., Integrals representing general hypergeometric transformations; Quart. J. Math., 2(3), 206-216 (1952).Slater, L. J., Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, England (1966).Somorjai, R. L. y D. M. Bishop, Integral transformation trial functions of the fractional integral class; Phys. Rev., A1, 1013-1026 (1970).Sonine, N.Ya., Report on differentiation with an arbitrary index; (Ru-ssian), Proc. Second Congress of Russian Naturalists, 2, 18-21 (1870).Srivastava, H. M. y P. W. Karlsson, Multiple Gaussian Hypergeometric Series, John Wiley & Sons, New York, USA (1985).Srivastava H. M. y A. K. Agarwal, Generating functions for a class of q-polynomials; Annali di Matematica Pura ed Applicata, IV(154), 99-109 (1989).Sulaiman, W. T., On some new fractional q-integral inequalities; South Asian J. of Math., 2(5), 450-459 (2012).Tarasov, V. E., Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, New York, USA (2011).Thomae, J., Beitr¨age zur Theorie der durch die Heinesche Reihe: 1 + [(1−qα) 1−qβ ]/[(1−q)(1−qγ)] x + ... darstellbaren Functionen; J. reine angew. Math. 70, 258-281 (1869).Vinagre, B. M. y C. A. Monje, Introducci´on al control fraccionario; Rev. Iberoam. de Autom´at. e Inform. Indust., 3(3), 5-23 (2006).Weber y H. Dover (Eds.), Versuch einer allgemeinen auffasung der integration und differentiation, The collected works of Bernhard Riemann, New York, USA (1953).Wei, Z., W. Dong y J. Che, Periodic boundary value problems for fractional differential equations involving a Riemann Liouville fractional derivative; Nonlinear Analysis, 73, 3232-3238 (2010).West, B. J., M. Bologna y P. Grigolini, Physics of Fractal Operators, Springer, New York, USA (2003).Weyl, H., Bemerkungen zum begriff des differentialquotienten gebrochener ordnung; Vierteljschr. Naturforsch. Gesellsch. Zu¨rich, 62, 296-302 (1917).Whipple, F. J. W., On well-poised series, generalized hypergeometric series having parameters in pairs, each pair with the same sum; Proc. London math. Soc., 2(24), 247-263 (1926).Whipple, F. J. W., Well-poised series, and other generalized hypergeometric series; Proc. London math. Soc., 2(25), 525-544 (1926).Whipple, F. J. W., Algebraic proofs of the theorems of Cayley and Orr concerning the products of certain hypergeometric series; J. London Math. Soc., 2, 85-90 (1927).Whipple, F. J. W., On a formula implied in Orr’s theorems concerning the product of hypergeometric series; J. London Math., Soc., 4, 48-50 (1929).Wiener, N., The operational calculus; Math. Ann., 95, 557-584 (1926).Yadav, R. K. y S. D. Purohit, Application of Riemann-Liouville fractional q-integral operator to basic hypergeometric functions; Acta Ciencia Indica, 30(iii), 593-600 (2004).Yadav, R. K. y S. D. Purohit, On applications of Kober fractional q-integral operator to certain basic hypergeometric functions; J. Rajasthan Acad. Phy. Sci. 5(4), 437-448 (2006).Yadav, R. K. y S. D. Purohit, On applications of Weyl fractional q-integral operator to generalized basic hypergeometric functions; Kyungpook Math. J., 46, 235-245 (2006).Yadav, R. K., S. D. Purohit y S. L. Kalla, On generalized Wely fractional q-integral operator involving generalized basic hypergeometric functions; Fractional Calculus & Applied Analysis, 11(2), 129-142 (2008).Yadav, R. K., S. L. Kalla y G. Kaur, On fractional q-integral operator involving the basic multiple hypergeometric functions; Algebras Groups and Geometries, 27(1), 97-116 (2010).Zhu, C., W. Yang y O. Zhao, Some new fractional q-integral Gru¨ss-type inequalities and other inequalities; J. of Inequal. and Appl., Vol. 2012, article 299, 2012, DOI: 10.1186/1029-242X-2012-299.CálculoFuncionesAnálisis funcionalTeoría de los operadoresPublicationORIGINAL150. 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.


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