Dirichlet Average of Extended Mainardi Function and Fractional Derivative

Abstract

Abstract

In this paper, we establish a relation of Dirichlet average of Extended Mainardi function, using fractional derivative. The fractional calculus deals with integrals and derivatives of arbitrary order. Special roles in the applications of fractional calculus operators are played by the transcendental function of the Mittag-Leffler, generalized M-series function, M-function Generalized Miller-Ross function, Wright’s functions and more generally by the Meijer’s G-functions, Fox’s H-functions and Saxena’s I-function.  

Mathematics Subject Classification: 26A33, 33A30, 33A25 and 83C99

Keywords: Dirichlet average, Mainardi function, Extended Mainardi function fractional derivative and Fractional calculus operators