Identities on fractional integrals and various integral transforms (Q884164)

There is an important property relating the Laplace transform to integration, \(L\{\frac{f(t)}{t}\}=\int^\infty_sF(x)dx\). The author extends this identity to Weyl's fractional integration. In this spirit, he provides several interesting theorems relating the Weyl fractional integral and the Riemann-Liouville fractional integral to some classical integral transforms -- the Laplace, Stieltjes, Hankel, Widder potential transforms and the \(K\)-transform. As application, some interesting infinite integrals are evaluated involving elementary and special functions.