Identities on fractional integrals and various integral transforms

In this work we will introduce theorems relating the Riemann-Liouville fractional integral and the Weyl fractional integral to some well-known integral transforms including Laplace transforms, Stieltjes transforms, generalized Stieltes transforms, Hankel transforms, and K-transforms. As applications of the theorems and their results, a number of infinite integrals of elementary functions and special functions are evaluated and some illustrative examples are presented.