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:
- Hipergeométrico
Función generadora
Hipergeométrico ponderado
Polinomios de Srivastava
- 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 Hipergeométrico Función generadora Hipergeométrico ponderado Polinomios de Srivastava |
| 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.contributor.researchgroup.spa.fl_str_mv |
Modelación con Ecuaciones Diferenciales |
| dc.subject.proposal.spa.fl_str_mv |
Hipergeométrico Función generadora Hipergeométrico ponderado Polinomios de Srivastava |
| topic |
Hipergeométrico Función generadora Hipergeométrico ponderado Polinomios de Srivastava |
| 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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Artículo de investigación |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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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 |
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1687-1839 |
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http://hdl.handle.net/10495/22104 |
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10.1186/s13662-017-1165-7 |
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1687-1847 |
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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 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 |
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eng |
| dc.relation.ispartofjournalabbrev.spa.fl_str_mv |
Adv Differ Equ |
| dc.relation.citationendpage.spa.fl_str_mv |
11 |
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1 |
| dc.relation.citationvolume.spa.fl_str_mv |
105 |
| dc.relation.ispartofjournal.spa.fl_str_mv |
Advances in Difference Equations |
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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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Springer Open |
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Restrepo Tangarife, Joel EstebanKılıçman, AdemAgarwal, PraveenAltun, OmerModelación con Ecuaciones Diferenciales2021-09-03T00:27:03Z2021-09-03T00:27:03Z2017Restrepo, 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.11application/pdfengSpringer OpenEstados Unidoshttp://creativecommons.org/licenses/by/2.5/co/https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Weighted hypergeometric functions and fractional derivativeArtículo de investigaciónhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionHipergeométricoFunción generadoraHipergeométrico ponderadoPolinomios de SrivastavaAdv Differ Equ111105Advances in Difference EquationsPublicationORIGINALRestrepoJoel_2017_WeightedHypergeometricFunctions.pdfRestrepoJoel_2017_WeightedHypergeometricFunctions.pdfArtículo de investigaciónapplication/pdf1375614https://bibliotecadigital.udea.edu.co/bitstreams/4659c14b-d321-43fb-af6d-1d4c5f9775b7/downloadb34df120d4a192499a2b278e97f66e8aMD51trueAnonymousREADCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927https://bibliotecadigital.udea.edu.co/bitstreams/789fb945-c0e1-451e-ba9e-b8d600f4cbfb/download1646d1f6b96dbbbc38035efc9239ac9cMD52falseAnonymousREADLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstreams/743992e4-cf93-4e54-a12d-aad1c1a13891/download8a4605be74aa9ea9d79846c1fba20a33MD53falseAnonymousREADTEXTRestrepoJoel_2017_WeightedHypergeometricFunctions.pdf.txtRestrepoJoel_2017_WeightedHypergeometricFunctions.pdf.txtExtracted texttext/plain29087https://bibliotecadigital.udea.edu.co/bitstreams/a3e3ef2a-7a8e-4e8a-9fe2-a1509d00b6fc/downloadc87906806e3dc8abf59b4c6fa4db2f00MD54falseAnonymousREADTHUMBNAILRestrepoJoel_2017_WeightedHypergeometricFunctions.pdf.jpgRestrepoJoel_2017_WeightedHypergeometricFunctions.pdf.jpgGenerated Thumbnailimage/jpeg12350https://bibliotecadigital.udea.edu.co/bitstreams/dbf68356-b35f-4a9a-9773-7f6118614990/download51b8d6b1ea5b69a3c36f3a71fa8ff814MD55falseAnonymousREAD10495/22104oai:bibliotecadigital.udea.edu.co:10495/221042025-03-26 21:29:31.704http://creativecommons.org/licenses/by/2.5/co/open.accesshttps://bibliotecadigital.udea.edu.coRepositorio Institucional de la Universidad de Antioquiaaplicacionbibliotecadigitalbiblioteca@udea.edu.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 |