A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms
The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that pro...
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| Veröffentlicht in: | Journal of Mathematics Jg. 2022; H. 1 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Cairo
Hindawi
2022
John Wiley & Sons, Inc Wiley |
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| ISSN: | 2314-4629, 2314-4785 |
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| Abstract | The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss hypergeometric functions and the extension of new confluent hypergeometric functions. Moreover, discussed are analogous statements in terms of the Weyl, Riemann–Liouville, Erdélyi–Kober, and Saigo fractional integral and derivative operator types. Here, we are also able to generate more image formulas by keeping some integral transforms on the obtained formulas. |
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| AbstractList | The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss hypergeometric functions and the extension of new confluent hypergeometric functions. Moreover, discussed are analogous statements in terms of the Weyl, Riemann–Liouville, Erdélyi–Kober, and Saigo fractional integral and derivative operator types. Here, we are also able to generate more image formulas by keeping some integral transforms on the obtained formulas. |
| Audience | Academic |
| Author | Palsaniya, Vandana Suthar, D. L. Joshi, Sunil Mittal, Ekta |
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| Cites_doi | 10.3934/dcdss.2020030 10.1016/j.amc.2003.09.017 10.1002/num.22601 10.1155/2018/6451592 10.1007/s13370-020-00848-4 10.1155/2021/8353719 10.1007/s40819-021-01181-5 10.1007/s40009-020-00996-y 10.1007/s40819-017-0410-9 10.1016/j.cam.2010.04.019 10.1007/s40819-019-0750-8 10.1155/2019/6487687 10.22436/jnsa.008.05.01 10.1080/23311835.2017.1320830 10.1016/0377-0427(94)90187-2 10.1016/s0377-0427(96)00102-1 |
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| Copyright | Copyright © 2022 Vandana Palsaniya et al. COPYRIGHT 2022 John Wiley & Sons, Inc. Copyright © 2022 Vandana Palsaniya et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Applied mathematics Derivatives Fractional calculus Hypergeometric functions Integral transforms Integrals Laplace transforms Mathematical functions Mathematics Operators (mathematics) Partial differential equations Theorems |
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| Title | A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms |
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