On the p-k-Mittag-Leffler function

Abstract

In this paper, we define the function pEk;;(z), estudy its analyticproperties, some elementary properties as its integral expression,its relationship with the fractional operator of Riemann-Liouville and investigatethe fractional generalization of the kinetic equation involvingthis Mittag-Leffler type function. This new Mittag-Leffler-type functionrelated to the two parameters Gamma function recently introducedby Gehlot [8], is a generalizaton of the k-Mittag-Leffler function sincek􀀀k(z) = 􀀀k(z), thus generalize the Mittag-Leffler of two parameter,Mittag-Leffler function and the exponential function.