@article{Srivastava_Bansal_Harjule_2023, title={A class of fractional integral operators involving a certain general multiindex Mittag-Leffler function }, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/863}, DOI={10.3842/umzh.v75i8.863}, abstractNote={<p class="p1">UDC 517.9</p> <p class="p1">This paper is essentially motivated by the demonstrated potential for applications of the presented results in<span class="Apple-converted-space"> </span>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<span class="Apple-converted-space"> </span>involving a certain general<span class="Apple-converted-space"> </span>family of multiindex Mittag-Leffler functions in their kernel. Among other results obtained in the paper,<span class="Apple-converted-space"> </span>we establish several interesting expressions<span class="Apple-converted-space"> </span>for the composition of well-known fractional integral<span class="Apple-converted-space"> </span>and fractional derivative operators, such as (e.g.)<span class="Apple-converted-space"> </span>the Riemann–Liouville fractional<span class="Apple-converted-space"> </span>integral and fractional<span class="Apple-converted-space"> </span>derivative operators, the Hilfer<span class="Apple-converted-space"> </span>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<span class="Apple-converted-space"> </span>obtained in earlier investigations on this subject. We also present some potentially useful integral representations for<span class="Apple-converted-space"> </span>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.</p>}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Srivastava, H. M. and Bansal, Manish Kumar and Harjule, Priyanka}, year={2023}, month={Aug.}, pages={1096 - 1112} }