Fractional calculus formulas for Mathieu-type series and generalized Mittag-Leffler function

Abstract

Fractional calculus is allowing integrals and derivatives of any positive order (the term 'fractional' kept only for historical reasons), which can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where integrals are of convolution form with weakly singular kernels of power-law type. In recent decades fractional calculus has won more and more interest in applications in several fields of applied sciences. In this line, our main object to investigate image formulas of generalized fractional hypergeometric operators involving the product of Mathieu-type series and generalized Mittag-Leffler function. We also consider some interesting special cases of derived results by specializing suitable value of the parameters.