FRACTIONAL CALCULUS OPERATORS OF THE GENERALIZED EXTENDED MITTAG-LEFFLER FUNCTION AND RELATED JACOBI TRANSFORMS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 103
DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.10
Author :
Shilpa Kumawat (Department of Mathematics, Career Point University, Kota - 325003, Rajasthan, INDIA)
Hemlata Saxena (Department of Mathematics, Career Point University, Kota - 325003, Rajasthan, INDIA)
Purnima Chopra (Formerly Department of Mathematics, Marudhar Engineering College, Bikaner - 334001, Rajasthan, INDIA)
Abstract
Our aim is to obtain certain image formulas of the $p$--extended Mittag-Leffler function $\mathcal{E}_{\alpha,\beta,p}^{\gamma}(z) $ by using Saigo's hypergeometric fractional integral and differential operators. Corresponding assertions for the classical Riemann-Liouville (R-L) and Erd\'elyi-Kober (E-K) fractional integral and differential operators are established. All the results are represented in terms of the Hadamard product of the $p$--extended Mittag-Leffler function $\mathcal{E}_{\lambda,\mu,p}^{\gamma}(z) $ and Fox-Wright function $_{r}\Psi_{s}(z)$. We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the $p$--extended Mittag-Leffler function $\mathcal{E}_{\alpha,\beta,p}^{\gamma}(z) $.
Keywords and Phrases
Fractional Calculus operators, Fox-Wright function, Generalized hypergeometric function, Extended Mittag-Leffler function, Gegenbauer and Legendre transforms.
A.M.S. subject classification
Primary 26A33, 33B20, 33C20; Secondary 26A09, 33B15, 33C05.
.....
