M-Srivastava hypergeometric functions: integral representations and solution of fractional differential equations

Abstract

In this paper, we introduce a new extensions of Srivastava’s triple hypergeometric functions HA, HB and HC, by using an modified beta function, which given with a generalized M-series in its kernel. We also introduce a new extension of Appell’s hypergeometric function of the first kind by using the same modified beta function. Furthermore, we give some integral representations of the new extensions of Srivastava’s triple hypergeometric functions. Finally, we obtain solutions of fractional differential equations involving new extensions of Srivastava’s triple hypergeometric functions.