SOLUTION OF A GENERAL FAMILY OF FRACTIONAL KINETIC EQUATIONS ASSOCIATED WITH THE GENERALIZED MITTAG-LEFFLER FUNCTION

Abstract

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving such special functions as (for example) a generalized Bessel function of the first kind [18] and the Aleph function [6]. Here, in this paper, we aim at presenting solution of a certain general family of fractional kinetic equations associated with the generalized Mittag- Leffler function. It is also shown that the result presented here includes, as its special cases, solutions of many fractional kinetic equations which were investigated in earlier works. In our investigation, we have found it to be more convenient to use (and the closed-form results derived here appear to be considerably simpler by using) the Sumudu transform instead of the classical Laplace transform.