Fractional differential equations for the generalized Mittag-Leffler function

Abstract

In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.