Mellin transform for fractional integrals with general analytic kernel

Abstract

<abstract><p>Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order $ \varsigma\ge0 $ and $ \varrho $ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.</p></abstract>