Fractional calculus of modified special functions involving the generalized M-series in their kernels and illustrative examples

In this paper we apply the Riemann–Liouville, Erdelyi-Kober and Caputo fractional operators to modified beta, Gauss hypergeometric and confluent hypergeometric functions in which the generalized M-series are included in their kernels. Furthermore, as examples, we obtain solutions of some fractional differential equations involving the above modified special functions.