The Classical Sumudu Transform and its q-Image of the Most Generalized Hypergeometric and Wright-Type Hypergeometric Functions

Abstract

The q- Calculus has served as a bridge between mathematics and physics, particularly in case of quantum physics. The q-generalizations of mathematical concepts like Laplace, Fourier and Sumudu transforms, Hypergeometric functions etc. can be advantageously used in solution of various problems arising in the field of physical and engineering sciences. The q-Sumudu transform, the q-image of classical Sumudu transform is the theoretical dual of the q-Laplace transform. In view of this, the present paper deals with some of the important applications of classical Sumudu and q-Sumudu transform of generalized hypergeometric function and Wright-type hypergeometric function. The results have been presented in terms of well-known Fox’s H-function. Some special cases have also been discussed.