Fractional Integration and Fractional Differentiation of the Product of M-Series and H-Function

Abstract

In this paper, we have derived formulae for the Riemann-Liouville fractional integral and fractional derivative of the product of the Manoj Sharma’s M-series and the Fox H-function.  Also the fractional integrals defined  by  Saxena and Kumbhat of the M-series is found with the help of integral of H-function. The M- series is a particular case of the -function of Inayat-Hussain. Certain special cases of the formulae have also been discussed.

Mathematics Subject classification: 26A33, 33C60.

Keywords and Phrases: Fractional calculus operators, H-function, M-series, Laplace transform.