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

Abstract

In this paper we apply the Riemann–Liouville, Erdelyi–Kober and Caputo fractional operators to the modified beta, modified Gauss hypergeometric and modified 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.

Keywords

• Fractional derivatives and integrals
• Fractional differential equations
• Beta function
• Gauss hypergeometric function
• Confluent hypergeometric function