A class of generalized Mittag-Leffler-type functions associated with the Lauricella functions of three variable
Annotatsiya
In this article, we aim to study the Mittag-Leffler-type functions ~F(3)A , ~F(3) B , ~F(3) C and ~F(3) D , which correspond, respectively, to the familiar Lauricella hypergeometric functions F(3) A , F(3) B , F(3) C and F(3) D of three variables. Amongthe various properties and characteristics of these three-variable Mittag-Leffler-type functions, which we investigate in this article, include their relationships with other extensions and generalizations of the classical Mittag-Leffler functions, their three-dimensional convergence regions, the systems of partial differential equations which are are satisfied by them, their Euler-type integral representations, their one- as well as three-dimensional Laplace transforms, and their connections with the Riemann-Liouville operators of fractional calculus.