On the Solution of General Family of Fractional Differential Equation Involving Hilfer Derivative Operator and $\overline{H}$-function

Abstract

In this paper, we first give solution to a general family of fractional differential equation involving Hilfer derivative operator and the fractional integral operator whose kernel is the $\overline{H}$-function. Next, we record here solutions of two fractional differential equations involving the function associated with Gaussian Model free energy and Polylogarithm function of order g as special cases of our main result. These special cases are believed to be new. On account of the general nature of\, $\overline{H}$-function in our main findings, the results derived earlier by Srivastava et al. [15], Srivastava and Tomovski [16] and Tomovski et al. [17] follow as special cases.