A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators

Abstract

In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters. We also define new generalizations of the Gauss F, Appell $F_{1}$ , $F_{2}$ and Lauricella $F_{D}^{3}$ hypergeometric functions with the help of new beta function. Then we obtain some generating function relations for these generalized hypergeometric functions by using each generalized fractional operators, separately. One of the purposes of the present investigation is to give a chance to the reader to compare the results corresponding to each generalized fractional operators.