Κ -Fractional Calculus Operators and Solution of Fractional Kinetic Equations Involving the Multivariate Κ -Mittag-Leffler Matrix Functions

Abstract

In this paper, a matrix analogue of a new generalization of multivariate κ-Mittag-Leffler (M-L) function is introduced. The differential and integral formulas and the κ-fractional calculus operator for the generalized multivariate κ-M-L matrix function are obtained. The κ-Beta and Mellin transforms are presented for the generalized multivariate κ-M-L matrix function. Finally, the solution of the fractional kinetic equation involving the new multivariate κ-M-L matrix function is provided as an application.