The Joint Laplace-Hankel Transforms for Fractional Diffusion Equation

Operational methods are used to accomplish the solution of certain problems with less effort and in a simple routine way. Laplace transforms can be used to solve certain types of fractional singular integral equation not considered in the literature. In this study, the author implemented an analytical technique the joint Laplace-Hankel transforms to provide the exact solution for a time fractional non-homogeneous diffusion equation with non-constant coefficients in cylindrical coordinates. The obtained results reveal that the joint transform method is very convenient and effective. Certain non trivial integral identities involving Airy functions and modified Bessel functions of the second kind are also provided.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).