Identities on fractional integrals and various integral transforms

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摘要

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.

论文关键词：Parseval–Goldstein type of identities,Riemann–Liouville fractional integral,Weyl fractional integral,Fractional derivatives,Laplace transform,Widder potential transform,Stieltjes transform,Generalized Stieltjes transform,Hankel transform,K-transform,Bessel functions,Modified Bessel functions of the third kind,Exponential integral function,Error function,Complementary error function

论文评审过程：Available online 11 October 2006.

论文官网地址：https://doi.org/10.1016/j.amc.2006.09.001