Some identities on fractional integrals and integral transforms

Year 2020, Volume: 49 Issue: 1, 8 - 18, 06.02.2020

Nese Dernek , Gülçin Bozkurt

https://doi.org/10.15672/HJMS.2018.652

Abstract

In this paper, we introduce various theorems that associate the generalized Riemann-Liouville fractional integral operator and the generalized Weyl fractional integral operator with some well-known integral transforms including generalized Laplace transform, Widder potential transform, generalized Widder transform, Hankel transform and Bessel transform. We evaluate certain integrals of some elementary functions and some special functions as applications of these theorems and their results.

Keywords

Riemann-Liouville fractional integral, Weyl fractional integral, fractional derivatives, Laplace transform, Widder potential transform, Hankel transform, Bessel transform, error function, exponential integral function

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