Extended Riemann-Liouville type fractional derivative operator with applications
The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeomet...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2017-0137 |
| _version_ | 1818358402179399680 |
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| author | Agarwal P. Nieto Juan J. Luo M.-J. |
| author_facet | Agarwal P. Nieto Juan J. Luo M.-J. |
| author_sort | Agarwal P. |
| collection | DOAJ |
| description | The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented. |
| first_indexed | 2024-12-13T20:28:26Z |
| format | Article |
| id | doaj.art-3c9ebf90ad0547eaaf4af769c595d267 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-13T20:28:26Z |
| publishDate | 2017-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-3c9ebf90ad0547eaaf4af769c595d2672022-12-21T23:32:29ZengDe GruyterOpen Mathematics2391-54552017-12-011511667168110.1515/math-2017-0137math-2017-0137Extended Riemann-Liouville type fractional derivative operator with applicationsAgarwal P.0Nieto Juan J.1Luo M.-J.2Department of Mathematics, Anand International College of Engineering, Jaipur-303012, Republic of IndiaDepartamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticasd, Universidade de Santiago de Compostela, 15782Santiago de Compostela, SpainDepartment of Mathematics, East China Normal University, Shanghai200241, ChinaThe main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.https://doi.org/10.1515/math-2017-0137gamma functionextended beta functionriemann-liouville fractional derivativehypergeometric functionsfox h-functiongenerating functionsmellin transformintegral representations26a3333b1533b2033c0533c2033c65 |
| spellingShingle | Agarwal P. Nieto Juan J. Luo M.-J. Extended Riemann-Liouville type fractional derivative operator with applications Open Mathematics gamma function extended beta function riemann-liouville fractional derivative hypergeometric functions fox h-function generating functions mellin transform integral representations 26a33 33b15 33b20 33c05 33c20 33c65 |
| title | Extended Riemann-Liouville type fractional derivative operator with applications |
| title_full | Extended Riemann-Liouville type fractional derivative operator with applications |
| title_fullStr | Extended Riemann-Liouville type fractional derivative operator with applications |
| title_full_unstemmed | Extended Riemann-Liouville type fractional derivative operator with applications |
| title_short | Extended Riemann-Liouville type fractional derivative operator with applications |
| title_sort | extended riemann liouville type fractional derivative operator with applications |
| topic | gamma function extended beta function riemann-liouville fractional derivative hypergeometric functions fox h-function generating functions mellin transform integral representations 26a33 33b15 33b20 33c05 33c20 33c65 |
| url | https://doi.org/10.1515/math-2017-0137 |
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