Fractional differential equations for the generalized Mittag-Leffler function

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(⋅)$F_{3}(\cdot)$ and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p)${}_{m+1}\psi^{(\{\kappa_{l}\}_{l\in\mathbb{N}_{0}} )}_{n+1}(z; p)$ recently established by Agarwal. Some interesting special cases are also pointed out.

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