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Novel Kinds of Fractional λ –Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral

Author

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  • Mohammed Z. Alqarni

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • Mohamed Abdalla

    (Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
    These authors contributed equally to this work.)

Abstract

In recent years, fractional kinetic equations (FKEs) involving various special functions have been widely used to describe and solve significant problems in control theory, biology, physics, image processing, engineering, astrophysics, and many others. This current work proposes a new solution to fractional λ − kinetic equations based on generalized degenerate hypergeometric functions (GDHFs), which has the potential to be applied to calculate changes in the chemical composition of stars such as the sun. Furthermore, this expanded form can also help to solve various problems with phenomena in physics, such as fractional statistical mechanics, anomalous diffusion, and fractional quantum mechanics. Moreover, some of the well-known outcomes are just special cases of this class of pathway-type solutions involving GDHFs, with greater accuracy, while providing an easily calculable solution. Additionally, numerical graphs of these analytical solutions, using MATLAB Software (latest version 2023b), are also considered.

Suggested Citation

  • Mohammed Z. Alqarni & Mohamed Abdalla, 2023. "Novel Kinds of Fractional λ –Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral," Mathematics, MDPI, vol. 11(19), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4217-:d:1256263
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    References listed on IDEAS

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    1. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
    2. Fuli He & Ahmed Bakhet & Mohamed Akel & Mohamed Abdalla, 2020. "Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
    3. Hafte Amsalu & Biniyam Shimelis & D. L. Suthar, 2020. "Pathway Fractional Integral Formulas Involving - Function in the Kernel," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-6, June.
    4. Saxena, R.K. & Mathai, A.M. & Haubold, H.J., 2004. "On generalized fractional kinetic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 657-664.
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