ON THE CONSTRUCTION OF (p,k)-HYPERGEOMETRIC FUNCTION AND APPLICATIONS

In this paper, we construct a [Formula: see text]-hypergeometric function by using the Hadamard product, which we call the generalized [Formula: see text]-hypergeometric function. Several properties, namely, convergence properties, derivative formulas, integral representations and differential equations are indicated of this function. The latter function is a generalization of the usual hypergeometric function, the k-analogue of hypergeometric function and other hypergeometric functions are recently presented. As an application, we obtain the solution of the generalized fractional kinetic equations involving of the generalized [Formula: see text]-hypergeometric function.