A class of fractional integral operators involving a certain general multiindex Mittag-Leffler function

Abstract

UDC 517.9 This paper is essentially motivated by the demonstrated potential for applications of the presented results in  numerous widespread research areas, such as the mathematical, physical, engineering, and statistical sciences. The main object here is to introduce and investigate a class of fractional integral operators  involving a certain general  family of multiindex Mittag-Leffler functions in their kernel. Among other results obtained in the paper,  we establish several interesting expressions  for the composition of well-known fractional integral  and fractional derivative operators, such as (e.g.)  the Riemann–Liouville fractional  integral and fractional  derivative operators, the Hilfer  fractional derivative operator, and the above-mentioned fractional integral operator involving the general family of multiindex Mittag-Leffler functions in its kernel. Our main result is a generalization of the results  obtained in earlier investigations on this subject. We also present some potentially useful integral representations for  the product of two members of the general family of multiindex Mittag-Leffler functions in terms of the well-known Fox–Wright hypergeometric function p Ψ q with p numerator and q denominator parameters.