On the p-k-mittag-leffler function

Abstract

In this paper, we define the function pE γ k,α,β(z), estudy its analytic properties, some elementary properties as its integral expression, its relationship with the fractional operator of Riemann-Liouville and investigate the fractional generalization of the kinetic equation involving this Mittag-Leffler type function. This new Mittag-Leffler-type function related to the two parameters Gamma function recently introduced by Gehlot [8], is a generalizaton of the k-Mittag-Leffler function since kΓk(z) = Γk(z), thus generalize the Mittag-Leffler of two parameter, Mittag-Leffler function and the exponential function.