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Analytic solutions to the fractional kinetic equation involving the generalized Mittag-Leffler function using the degenerate Laplace type integral approach

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Abstract

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.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a Large Group research project under grant number RGP2/25/44.

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  1. Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

    Yahya Almalki & Mohamed Abdalla

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  1. Yahya Almalki
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  2. Mohamed Abdalla
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Correspondence to Mohamed Abdalla.

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Almalki, Y., Abdalla, M. Analytic solutions to the fractional kinetic equation involving the generalized Mittag-Leffler function using the degenerate Laplace type integral approach. Eur. Phys. J. Spec. Top. 232, 2587–2593 (2023). https://doi.org/10.1140/epjs/s11734-023-00925-2

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