On the generating functions of the newly defined generalized hypergeometric functions

Abstract

In this paper, we have defined new generalizations of some hypergeometric functions and fractional operators with the help of Fox-Wright function. Then, using each of the generalized fractional operators, we derived linear and bilinear generating function relations for these functions. Finally, we have shown that the newly defined hypergeometric functions and fractional operators can be reduced to functions and operators presented in many studies in the literature by giving special values for their parameters.