FRACTIONAL CALCULUS OPERATORS OF THE GENERALIZED EXTENDED MITTAG-LEFFLER FUNCTION AND RELATED JACOBI TRANSFORMS

Shilpa Kumawat; Hemlata Saxena; Purnima Chopra

doi:10.56827/SEAJMMS.2023.1902.10

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

DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.10

Keywords: Fractional Calculus operators, Fox-Wright function, Generalized hypergeometric function, Extended Mittag-Leffler function, Gegenbauer and Legendre transforms.

Abstract

Our aim is to obtain certain image formulas of the p-extended Mittag- Leffler function EΓ Alpha,β,p(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 EΓ λ,μ,p(z) and Fox-Wright function rΨs(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the p-extended Mittag-Leffler function EΓ Alpha,β,p(z).