Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions
Abstract Motivated by a recent study on certain families of the incomplete H-functions (Srivastava et al. in Russ. J. Math. Phys. 25(1):116–138, 2018), we aim to investigate and develop several interesting properties related to product of a more general polynomial class together with incomplete Fox–...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03067-0 |
| _version_ | 1818335708544237568 |
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| author | K. Jangid R. K. Parmar R. Agarwal Sunil D. Purohit |
| author_facet | K. Jangid R. K. Parmar R. Agarwal Sunil D. Purohit |
| author_sort | K. Jangid |
| collection | DOAJ |
| description | Abstract Motivated by a recent study on certain families of the incomplete H-functions (Srivastava et al. in Russ. J. Math. Phys. 25(1):116–138, 2018), we aim to investigate and develop several interesting properties related to product of a more general polynomial class together with incomplete Fox–Wright hypergeometric functions Ψ q ( γ ) p ( t ) ${}_{p}\Psi _{q}^{(\gamma )}(\mathfrak{t})$ and Ψ q ( Γ ) p ( t ) ${}_{p}\Psi _{q}^{(\Gamma )}(\mathfrak{t})$ including Marichev–Saigo–Maeda (M–S–M) fractional integral and differential operators, which contain Saigo hypergeometric, Riemann–Liouville, and Erdélyi–Kober fractional operators as particular cases regarding different parameter selection. Furthermore, we derive several integral transforms such as Jacobi, Gegenbauer (or ultraspherical), Legendre, Laplace, Mellin, Hankel, and Euler’s beta transforms. |
| first_indexed | 2024-12-13T14:27:43Z |
| format | Article |
| id | doaj.art-02ac86be48274f768206e903e31e29ac |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T14:27:43Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-02ac86be48274f768206e903e31e29ac2022-12-21T23:41:54ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020111710.1186/s13662-020-03067-0Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functionsK. Jangid0R. K. Parmar1R. Agarwal2Sunil D. Purohit3Dept. of HEAS (Mathematics), Rajasthan Technical UniversityDept. of HEAS (Mathematics), University College of Engineering and TechnologyDept. of Mathematics, Malaviya National Institute of TechnologyDept. of HEAS (Mathematics), Rajasthan Technical UniversityAbstract Motivated by a recent study on certain families of the incomplete H-functions (Srivastava et al. in Russ. J. Math. Phys. 25(1):116–138, 2018), we aim to investigate and develop several interesting properties related to product of a more general polynomial class together with incomplete Fox–Wright hypergeometric functions Ψ q ( γ ) p ( t ) ${}_{p}\Psi _{q}^{(\gamma )}(\mathfrak{t})$ and Ψ q ( Γ ) p ( t ) ${}_{p}\Psi _{q}^{(\Gamma )}(\mathfrak{t})$ including Marichev–Saigo–Maeda (M–S–M) fractional integral and differential operators, which contain Saigo hypergeometric, Riemann–Liouville, and Erdélyi–Kober fractional operators as particular cases regarding different parameter selection. Furthermore, we derive several integral transforms such as Jacobi, Gegenbauer (or ultraspherical), Legendre, Laplace, Mellin, Hankel, and Euler’s beta transforms.http://link.springer.com/article/10.1186/s13662-020-03067-0Incomplete Fox–Wright functionsFractional calculus operatorsIntegral transforms |
| spellingShingle | K. Jangid R. K. Parmar R. Agarwal Sunil D. Purohit Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions Advances in Difference Equations Incomplete Fox–Wright functions Fractional calculus operators Integral transforms |
| title | Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions |
| title_full | Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions |
| title_fullStr | Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions |
| title_full_unstemmed | Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions |
| title_short | Fractional calculus and integral transforms of the product of a general class of polynomial and incomplete Fox–Wright functions |
| title_sort | fractional calculus and integral transforms of the product of a general class of polynomial and incomplete fox wright functions |
| topic | Incomplete Fox–Wright functions Fractional calculus operators Integral transforms |
| url | http://link.springer.com/article/10.1186/s13662-020-03067-0 |
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