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

H. M.  Srivastava; Manish Kumar Bansal; Priyanka Harjule

doi:10.3842/umzh.v75i8.863

H. M. Srivastava Department of Mathematics and Statistics, University of Victoria, British Columbia, Canada, Department of Medical Research, China Medical University Hospital, China Medical University, Taiwan, Republic of China and Department of Mathematics and Informatics, Azerbaijan University, Baku https://orcid.org/0000-0002-9277-8092
Manish Kumar Bansal Department of Mathematics, Government Engineering College, Rajasthan, India
Priyanka Harjule Department of Mathematics, Indian Institute of Information Technology, Rajasthan, India

DOI: https://doi.org/10.3842/umzh.v75i8.863

Keywords: 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 $\;_p\Psi_q$ with $p$ numerator and $q$ denominator parameters.

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