The Extended Multi-Index Mittag-Leffler Functions and Their Properties Connected with Fractional Calculus and Integral Transforms

Praveen Agarwal, D.L. Suthar, Shilpi Jain, Shaher Momani

Abstract

The aim of this paper to present the extended multi-index MittagLeffer type functions while using the extended Beta function and investigate several properties including, Integral representation, Derivatives, Beta
transform, Mellin transform, Relationships between this function with the
Leguerre polynomials and Whittakar functions. Further, several properties
of the Riemann-Liouville fractional derivative and integral operators related
to extended multi-index Mittag-Leffer functions are also investigated. Finally,
various interesting special cases of these function have also pointed out.