Weighted hypergeometric functions and fractional derivative
ABSTRACT: We introduce some weighted hypergeometric functions and the suitable generalization of the aputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator. Then some of the considered hypergeomet...
- Autores:
-
Restrepo Tangarife, Joel Esteban
Kılıçman, Adem
Agarwal, Praveen
Altun, Omer
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2017
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/22104
- Acceso en línea:
- http://hdl.handle.net/10495/22104
- Palabra clave:
- Weighted Caputo fractional derivative
Weighted hypergeometric function
Generating function
Srivastava polynomials
Generalized Mittag-Leffler function
α-capacity
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
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| dc.title.spa.fl_str_mv |
Weighted hypergeometric functions and fractional derivative |
| title |
Weighted hypergeometric functions and fractional derivative |
| spellingShingle |
Weighted hypergeometric functions and fractional derivative Weighted Caputo fractional derivative Weighted hypergeometric function Generating function Srivastava polynomials Generalized Mittag-Leffler function α-capacity |
| title_short |
Weighted hypergeometric functions and fractional derivative |
| title_full |
Weighted hypergeometric functions and fractional derivative |
| title_fullStr |
Weighted hypergeometric functions and fractional derivative |
| title_full_unstemmed |
Weighted hypergeometric functions and fractional derivative |
| title_sort |
Weighted hypergeometric functions and fractional derivative |
| dc.creator.fl_str_mv |
Restrepo Tangarife, Joel Esteban Kılıçman, Adem Agarwal, Praveen Altun, Omer |
| dc.contributor.author.none.fl_str_mv |
Restrepo Tangarife, Joel Esteban Kılıçman, Adem Agarwal, Praveen Altun, Omer |
| dc.subject.proposal.spa.fl_str_mv |
Weighted Caputo fractional derivative Weighted hypergeometric function Generating function Srivastava polynomials Generalized Mittag-Leffler function α-capacity |
| topic |
Weighted Caputo fractional derivative Weighted hypergeometric function Generating function Srivastava polynomials Generalized Mittag-Leffler function α-capacity |
| description |
ABSTRACT: We introduce some weighted hypergeometric functions and the suitable generalization of the aputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator. Then some of the considered hypergeometric functions are determined in terms of the generalized Mittag-Leffler function E (γj),(lj) (ρj),λ [z1, ... ,zr] (Mainardi in Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, 2010) and the generalized polynomials Sm n [x] (Srivastava in Indian J. Math. 14:1-6, 1972). The boundary behavior of some other class of weighted hypergeometric functions is described in terms of Frostman’s α-capacity. Finally, an application is given using our fractional operator in the problem of fractional calculus of variations. |
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2017 |
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2017 |
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2021-09-03T00:27:03Z |
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2021-09-03T00:27:03Z |
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info:eu-repo/semantics/article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Artículo de investigación |
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Restrepo, J., Kılıçman, A., Agarwal, P., et al. (2017) Funciones hipergeométricas ponderadas y derivada fraccionaria. Adv Differ Equ. 105, 1-11. https://doi.org/10.1186/s13662-017-1165-7 |
| dc.identifier.issn.none.fl_str_mv |
1687-1839 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10495/22104 |
| dc.identifier.doi.none.fl_str_mv |
10.1186/s13662-017-1165-7 |
| dc.identifier.eissn.none.fl_str_mv |
1687-1847 |
| identifier_str_mv |
Restrepo, J., Kılıçman, A., Agarwal, P., et al. (2017) Funciones hipergeométricas ponderadas y derivada fraccionaria. Adv Differ Equ. 105, 1-11. https://doi.org/10.1186/s13662-017-1165-7 1687-1839 10.1186/s13662-017-1165-7 1687-1847 |
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http://hdl.handle.net/10495/22104 |
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eng |
| language |
eng |
| dc.relation.ispartofjournalabbrev.spa.fl_str_mv |
Adv Differ Equ |
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info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by/2.5/co/ |
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https://creativecommons.org/licenses/by/4.0/ |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/co/ http://purl.org/coar/access_right/c_abf2 https://creativecommons.org/licenses/by/4.0/ |
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11 |
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application/pdf |
| dc.publisher.spa.fl_str_mv |
Springer Open |
| dc.publisher.group.spa.fl_str_mv |
Modelación con Ecuaciones Diferenciales |
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Estados Unidos |
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Universidad de Antioquia |
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andres.perez@udea.edu.co |
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Restrepo Tangarife, Joel EstebanKılıçman, AdemAgarwal, PraveenAltun, Omer2021-09-03T00:27:03Z2021-09-03T00:27:03Z2017Restrepo, J., Kılıçman, A., Agarwal, P., et al. (2017) Funciones hipergeométricas ponderadas y derivada fraccionaria. Adv Differ Equ. 105, 1-11. https://doi.org/10.1186/s13662-017-1165-71687-1839http://hdl.handle.net/10495/2210410.1186/s13662-017-1165-71687-1847ABSTRACT: We introduce some weighted hypergeometric functions and the suitable generalization of the aputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator. Then some of the considered hypergeometric functions are determined in terms of the generalized Mittag-Leffler function E (γj),(lj) (ρj),λ [z1, ... ,zr] (Mainardi in Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, 2010) and the generalized polynomials Sm n [x] (Srivastava in Indian J. Math. 14:1-6, 1972). The boundary behavior of some other class of weighted hypergeometric functions is described in terms of Frostman’s α-capacity. Finally, an application is given using our fractional operator in the problem of fractional calculus of variations.COL002436511application/pdfengSpringer OpenModelación con Ecuaciones DiferencialesEstados Unidosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Weighted hypergeometric functions and fractional derivativeWeighted Caputo fractional derivativeWeighted hypergeometric functionGenerating functionSrivastava polynomialsGeneralized Mittag-Leffler functionα-capacityAdv Differ EquAdvances in Difference Equations111105ORIGINALRestrepoJoel_2017_WeightedHypergeometricFunctions.pdfRestrepoJoel_2017_WeightedHypergeometricFunctions.pdfArtículo de investigaciónapplication/pdf1375614http://bibliotecadigital.udea.edu.co/bitstream/10495/22104/1/RestrepoJoel_2017_WeightedHypergeometricFunctions.pdfb34df120d4a192499a2b278e97f66e8aMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927http://bibliotecadigital.udea.edu.co/bitstream/10495/22104/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/22104/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/22104oai:bibliotecadigital.udea.edu.co:10495/221042021-09-02 19:27:04.085Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |