Pseudo asymptotic solutions of fractional order semilinear equations

Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of mild solutions for the semilinear fractional order differential equation [mathematical equation] with the property that the solution can be written as u = f+h where f belongs to the space of peri...

Full description

Autores:
Alvarez-Pardo, Edgardo
Lizama, Carlos
Tipo de recurso:
Fecha de publicación:
2013
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/12196
Acceso en línea:
https://hdl.handle.net/20.500.12585/12196
Palabra clave:
Asymptotic solutions
Generalized semigroup theory;
Pseudo
Sectorial operators
Two-term time fractional derivative
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/4.0/
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oai_identifier_str oai:repositorio.utb.edu.co:20.500.12585/12196
network_acronym_str UTB2
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repository_id_str
dc.title.es_CO.fl_str_mv Pseudo asymptotic solutions of fractional order semilinear equations
title Pseudo asymptotic solutions of fractional order semilinear equations
spellingShingle Pseudo asymptotic solutions of fractional order semilinear equations
Asymptotic solutions
Generalized semigroup theory;
Pseudo
Sectorial operators
Two-term time fractional derivative
title_short Pseudo asymptotic solutions of fractional order semilinear equations
title_full Pseudo asymptotic solutions of fractional order semilinear equations
title_fullStr Pseudo asymptotic solutions of fractional order semilinear equations
title_full_unstemmed Pseudo asymptotic solutions of fractional order semilinear equations
title_sort Pseudo asymptotic solutions of fractional order semilinear equations
dc.creator.fl_str_mv Alvarez-Pardo, Edgardo
Lizama, Carlos
dc.contributor.author.none.fl_str_mv Alvarez-Pardo, Edgardo
Lizama, Carlos
dc.subject.keywords.es_CO.fl_str_mv Asymptotic solutions
Generalized semigroup theory;
Pseudo
Sectorial operators
Two-term time fractional derivative
topic Asymptotic solutions
Generalized semigroup theory;
Pseudo
Sectorial operators
Two-term time fractional derivative
description Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of mild solutions for the semilinear fractional order differential equation [mathematical equation] with the property that the solution can be written as u = f+h where f belongs to the space of periodic (resp. almost periodic, compact almost automorphic, almost automorphic) functions and h belongs to the space [mathematical equation]. Moreover, this decomposition is unique.
publishDate 2013
dc.date.issued.none.fl_str_mv 2013
dc.date.accessioned.none.fl_str_mv 2023-07-19T21:19:13Z
dc.date.available.none.fl_str_mv 2023-07-19T21:19:13Z
dc.date.submitted.none.fl_str_mv 2023-07
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status_str draft
dc.identifier.citation.es_CO.fl_str_mv Edgardo, A.-P. , Lizama, C. Pseudo asymptotic solutions of fractional order semilinear equations (2013) Banach Journal of Mathematical Analysis, 7 (2), pp. 42-52. DOI: 10.15352/bjma/1363784222
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/12196
dc.identifier.doi.none.fl_str_mv 10.15352/bjma/1363784222
dc.identifier.instname.es_CO.fl_str_mv Universidad Tecnológica de Bolívar
dc.identifier.reponame.es_CO.fl_str_mv Repositorio Universidad Tecnológica de Bolívar
identifier_str_mv Edgardo, A.-P. , Lizama, C. Pseudo asymptotic solutions of fractional order semilinear equations (2013) Banach Journal of Mathematical Analysis, 7 (2), pp. 42-52. DOI: 10.15352/bjma/1363784222
10.15352/bjma/1363784222
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/12196
dc.language.iso.es_CO.fl_str_mv eng
language eng
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dc.rights.accessrights.es_CO.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.cc.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 11 páginas
dc.format.medium.none.fl_str_mv Pdf
dc.format.mimetype.es_CO.fl_str_mv application/pdf
dc.publisher.place.es_CO.fl_str_mv Cartagena de Indias
dc.source.es_CO.fl_str_mv Banach Journal of Mathematical Analysis - vol. 7 No. 2 (2013)
institution Universidad Tecnológica de Bolívar
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spelling Alvarez-Pardo, Edgardo34e3befe-54cf-4572-8597-9a681aeebb61Lizama, Carlos077c10a1-e22c-4c78-afec-b94f2709dc2d2023-07-19T21:19:13Z2023-07-19T21:19:13Z20132023-07Edgardo, A.-P. , Lizama, C. Pseudo asymptotic solutions of fractional order semilinear equations (2013) Banach Journal of Mathematical Analysis, 7 (2), pp. 42-52. DOI: 10.15352/bjma/1363784222https://hdl.handle.net/20.500.12585/1219610.15352/bjma/1363784222Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarUsing a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of mild solutions for the semilinear fractional order differential equation [mathematical equation] with the property that the solution can be written as u = f+h where f belongs to the space of periodic (resp. almost periodic, compact almost automorphic, almost automorphic) functions and h belongs to the space [mathematical equation]. Moreover, this decomposition is unique.11 páginasPdfapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Banach Journal of Mathematical Analysis - vol. 7 No. 2 (2013)Pseudo asymptotic solutions of fractional order semilinear equationsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_2df8fbb1Asymptotic solutionsGeneralized semigroup theory;PseudoSectorial operatorsTwo-term time fractional derivativeCartagena de IndiasAraya, D., Lizama, C. Almost automorphic mild solutions to fractional differential equations (2008) Nonlinear Analysis, Theory, Methods and Applications, 69 (11), pp. 3692-3705. Cited 173 times. doi: 10.1016/j.na.2007.10.004Arendt, W., Batty, C., Hieber, M., Neubrander, F. Vector-valued Laplace Transforms and Cauchy Problems (2001) Monographs in Mathematics, 96. Cited 350 times. Birkhäuser, BaselBazhlekova, E. (2001) Fractional Evolution Equations in Banach Spaces. Cited 553 times. Ph.D. Thesis, Eindhoven University of TechnologyBochner, S. Continuous mappings of almost automorphic and almost periodic functions (1964) Proc. Nat. Acad. Sci. USA, 52, pp. 907-910. Cited 195 times.Bochner, S. Uniform convergence of monotone sequences of functions (1961) Proc. Nat. Acad. Sci. USA, 47, pp. 582-585. Cited 71 times.Bochner, S. A new approach in almost-periodicity (1962) Proc. Nat. Acad. Sci. USA, 48, pp. 2039-2043. Cited 280 times.Bochner, S., Von Neumann, J. On compact solutions of operational-differential equations I (1935) Ann. Math, 36, pp. 255-290. Cited 42 times.De Andrade, B., Cuevas, C., Henr´iquez, E. Almost automorphic solutions of hyperbolic evolution equations (2012) Banach Journal of Mathematical Analysis, 6 (1), pp. 90-100. Cited 5 times. doi: 10.15352/bjma/1337014667Goreno, R., Mainardi, F. Fractional Calculus: Integral and Differential Equations of Fractional Order CIMS Lecture Notes. Cited 160 times. http://arxiv.org/0805.3823Heymans, N., Podlubny, I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives (2006) Rheologica Acta, 45 (5), pp. 765-771. Cited 518 times. doi: 10.1007/s00397-005-0043-5Hilfer, R. (2000) Applications of Fractional Calculus in Physics. Cited 6131 times. World Scientifc Publ. Co., SingaporeKeyantuo, V., Lizama, C., Warma, M. Asymptotic Behavior of Fractional Order Semilinear Evolution Equations. Cited 2 times.Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. (2006) Theory and Applications of Fractional Differential Equations. Cited 12243 times. Elsevier, AmsterdamLiang, J., Zhang, J., Xiao, T.-J. Composition of pseudo almost automorphic and asymptotically almost automorphic functions (2008) Journal of Mathematical Analysis and Applications, 340 (2), pp. 1493-1499. Cited 158 times. doi: 10.1016/j.jmaa.2007.09.065Liu, J.-h., Song, X.-q. Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations (2010) Journal of Functional Analysis, 258 (1), pp. 196-207. Cited 53 times. doi: 10.1016/j.jfa.2009.06.007Lizama, C. Regularized solutions for abstract Volterra equations (Open Access) (2000) Journal of Mathematical Analysis and Applications, 243 (2), pp. 278-292. Cited 157 times. http://www.elsevier.com/inca/publications/store/6/2/2/8/8/6/index.htt doi: 10.1006/jmaa.1999.6668Lizama, C. An operator theoretical approach to a class of fractional order differential equations (Open Access) (2011) Applied Mathematics Letters, 24 (2), pp. 184-190. Cited 44 times. doi: 10.1016/j.aml.2010.08.042Lizama, C., N'Guérékata, G.M. Bounded Mild Solutions for Semilinear Integro Differential Equations in Banach Spaces (2010) Integral Equations and Operator Theory, 68 (2), pp. 207-227. Cited 68 times. doi: 10.1007/s00020-010-1799-2N’Guérékata, G.M. (2001) Almost Automorphic and Almost Periodic Functions in Abstract Spaces. Cited 399 times. Kluwer Academic/Plenum Publishers, New YorkPodlubny, I. (1999) Fractional Differential Equations. Cited 24755 times. Academic Press, San DiegoPrüss, J. (1993) Evolutionary Integral Equations and Applications. Cited 738 times. Birkhäuser VerlagSamko, S.G., Kilbas, A.A., Marichev, O.I. (1993) Fractional Integrals and Derivatives: Theory and Applications. Cited 10351 times. Gordon and Breach, New York, Translation from the Russian edition, Nauka i Tekhnika, Minsk (1987)Stojanović, M., Gorenflo, R. Nonlinear two-term time fractional diffusion-wave problem (Open Access) (2010) Nonlinear Analysis: Real World Applications, 11 (5), pp. 3512-3523. Cited 27 times. doi: 10.1016/j.nonrwa.2009.12.012Xiao, T.-J., Liang, J., Zhang, J. Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces (2008) Semigroup Forum, 76 (3), pp. 518-524. Cited 162 times. doi: 10.1007/s00233-007-9011-yZhang, C.Y. (2003) Almost Periodic Type Functions and Ergodicity. Cited 232 times. Science Press, Kluwer Academic Publishers, New YorkZhang, C. Pseudo almost periodic solutions of some differential equations (1994) Journal of Mathematical Analysis and Applications, 181 (1), pp. 62-76. Cited 270 times. doi: 10.1006/jmaa.1994.1005Zhang, C.Y. Pseudo almost periodic solutions of some differential equations, II (1995) Journal of Mathematical Analysis and Applications, 192 (2), pp. 543-561. 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