DIRICHLET AVERAGE OF NEW GENERALIZATION OF GENERALIZED M-SERIES AND FRACTIONAL DERIVATIVE

Abstract

In this paper Dirichlet average of a new Special function called as New generalization of Generalized M-series [17] which is recently given by Ahmad Faraj , Tariq Salim , Safaa Sadek, Jamal Ismai [10] has been obtained. This series is a particular case of Fox's H-function and it is a Generalized case of Generalized M-series [6] defined by Author. The New Generalized M-series is interesting because the q p F -hyper geometric function and the Generalized  M Series  follow as its particular cases and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Mathematics Subject Classification: 26A33, 33A30, 33A25 and 83C99.