Theorem relating a certain generalized Weyl fractional integral with the Laplace transform and a class of Whittaker transforms

Abstract

In the present paper the authors prove a theorem which asserts an interesting relationship between the classical Laplace transform, a certain class of Whittaker transforms, and a Weyl fractional integral involving a general class of polynomials with essentially arbitrary coefficients. By specializing the various parameters involved, this general theorem would readily yield several (known or new) results involving simpler integral operators. It is also shown how the relationship asserted by the theorem can be applied to evaluate the generalized Weyl fractional integrals of various special functions.