Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

Abstract

In this paper, Parseval-Goldstein type theorems involving the G ̃n-integral transform which is modified from G_2n-integral transform [7] and the -integral transform [8] are examined. Then, theorems in this paper are shown to yield a number of new identities involving several well-known integral transforms. Using these theorems and their corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Generalizations of Riemann-Liouville and Weyl fractional integral operators are also defined. Some theorems relating generalized Laplace transform, generalized Widder Potential transform, generalized Hankel transform and generalized Bessel transform are obtained. Some illustrative examples are given as applications of these theorems and their results.