Generalized Fractional Integral Operators Involving Mittag-Leffler Function

Abstract

The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s $H$-function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and $K$-transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters.