M-Lauricella Hypergeometric Functions: Integral Representations and Solution of Fractional Differential Equations

Abstract

In this paper, using the modified beta function involving the gen-eralized M-series in its kernel, we describe new extensions for the Lauricella hypergeometric functions F(r) A, FB(r), FC(r) and F(r) D . Furthermore, we find various integral representations for the newly defined extended Lauricella hy-pergeometric functions. Then, we obtain solution of fractional differential equations involving new extensions of Lauricella hypergeometric functions, as examples.