https://doi.org/10.1140/epjs/s11734-023-00925-2
Regular Article
Analytic solutions to the fractional kinetic equation involving the generalized Mittag-Leffler function using the degenerate Laplace type integral approach
Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia
Received:
24
March
2023
Accepted:
2
July
2023
Published online:
2
August
2023
Recently, several fractional kinetic equations involving various special functions have been widely and usefully used in describing and solving diverse important problems in physics and astrophysics. In this work, we present solutions of fractional kinetic equations involving kinds of the generalized Mittag-Leffler functions as an application of the modified degenerate Laplace integral transform (MDLIT). The MDLIT is obtained by using the degenerate-type exponential function, which was introduced by YunJae Kim et al. (Symmetry 10:471, 2018) as a generalization of the classical Laplace transform. The MDLIT of some fundamental functions and distinct generalized special functions such as the generalized Mittag-Leffler functions, the generalized hypergeometric function, and the Wright generalized hypergeometric function are also established. Furthermore, the outcomes for the traditional Laplace transform are retrieved from our results as particular cases.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
