Certain Integral Representation and Fractional Derivatives Associated to a General Function Related to Hurwitz-Lerch Zeta Function

Abstract

In this paper, some integral representation and fractional derivatives of a general function are established. The general function studied in this paper unifies the Mittag-Leffler function and the Hurwitz-Lerch Zeta function. We have evaluated certain type of integrals involving the Mittag-Leffler function which gives the general function as resultant. As application of these results the integral representation and fractional derivatives for simpler function related to the Hurwitz-Lerch Zeta function are shown to be derived.