Certain properties of fractional calculus operators associated with M-series

Abstract

The present investigation deals with fractional calculus of the generalized M-series which is a further extension of both Mittag-Leer function and generalized hypergeometric function \({}_{p}F_{q}\) and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Certain relations that exist between M-series and the Riemann-Liouville fractional integrals and derivatives are investigated. It has been shown that the fractional integration and di erentiation operators transform such functions with power multipliers into the functions of the same form.