We study some properties of generalized multivariable Mittag-Leffler function. Also we establish two theorems, which give the images of this function under the generalized fractional integral operators involving Fox’s H-function as kernel. Relating affirmations in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some known special cases have also been mentioned in the concluding section.

In this paper, we establish modified Saigo fractional integral operators involving the product of a general class of multivariable polynomials and the multivariable H-function. The results established here are of general nature and provide extension of some results obtained recently by Saxena et al.

The aim of this study is to introduce new (presumed) generalized fractional integral operators involving I -function as a kernel. In addition, two theorems have been developed under these operators that provide an image formula for this generalized M -series and also to study the different properties of the generalized M -series. The corresponding assertions in terms of Euler and Laplace transform methods are presented. Due to the general nature of the I -function and the generalized M -series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.