A class of extended Mittag-Leffler functions and their properties related to integral transforms and fractional calculus

Abstract

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag-Leffler function by means of the extended Beta function. We then systematically investigate several properties of the extended Mittag-Leffler function, including, for example, certain basic properties, Laplace transform, Mellin transform and Euler-Beta transform. Further, certain properties of the Riemann-Liouville fractional integrals and derivatives associated with the extended Mittag-Leffler function are investigated. Some interesting special cases of our main results are also pointed out.