Nonlinear Functional Analysis and Applications Vol. 23, No. 3 (2018), pp. 455-471 ISSN: 1229-1595(print), 2466-0973(online) http://nfaa.kyungnam.ac.kr/journal-nfaa Copyright c  2018 Kyungnam University Press KUP ress SOLUTION OF A GENERAL FAMILY OF FRACTIONAL KINETIC EQUATIONS ASSOCIATED WITH THE GENERALIZED MITTAG-LEFFLER FUNCTION Dinesh Kumar 1 , Junesang Choi 2 and H. M. Srivastava 3 1 Department of Mathematics and Statistics Jai Narain Vyas University, Jodhpur 342005, Rajasthan, India e-mail: dinesh dino03@yahoo.com 2 Department of Mathematics Dongguk University, Gyeongju 38066, Republic of Korea e-mail: junesang@mail.dongguk.ac.kr 3 Department of Mathematics and Statistics, University of Victoria Victoria, British Columbia V8W 3R4, Canada and China Medical University Taiwan, Taichung 40402, Republic of China e-mail: harimsri@math.uvic.ca 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. 0 Received January 9, 2018. Revised April 17, 2018. 0 2010 Mathematics Subject Classification: 26A33, 33E12, 44A10, 33C65, 34A08. 0 Keywords: Generalized fractional kinetic equation, Laplace transform, Sumudu trans- form, generalized Mittag-Leffler function, fractional integral operator. 0 Corresponding author: J. Choi(junesang@mail.dongguk.ac.kr).