Multi-Index Le Roy Functions of Mittag-Leffler-Prabhakar Type

The so-called Special Functions of Fractional Calculus (SF of FC) became important tools of FC, as solutions of fractional order differential and integral equations and systems that model various phenomena from natural and applied sciences, and social events.Among them, recently we have introduced and studied the multi-index analogues of the Mittag-Leffler function that include a very long list of SF of FC.As a next step, here we introduce multi-index analogues of the Mittag-Leffler-Prabhakar type Le Roy functions (abbr.as multi-MLPR) with 4mindices.We emphasize on the relations between the multi-index Mittag-Leffler functions, Prabhakar function, Le Roy type functions and multi-index Mittag-Lefler functions of Le Roy type, and also with the hyper-Bessel functions and other SF, appearing as eigenfunctions of fractional analogues of the hyper-Bessel operators of Dimovski.