ON GENERALIZED WRIGHT’S HYPERGEOMETRIC FUNCTIONS AND FRACTIONAL CALCULUS OPERATORS

Abstract. In the present paper we first establish some basic re-sults for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators (integration and differentiation of arbitrary or-ders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright’s hyper-geometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright’s hypergeometric function, and its composition (and other related properties) with the fractional calculus operators are also investi-gated. 1. Introduction an