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Fractional Gauss Hypergeometric Power Series Method for Solving Fractional Partial Differential Equations

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  • Isaac Addai
  • Benedict Barnes
  • Isaac Kwame Dontwi
  • Kwaku Forkuoh Darkwah

Abstract

The Fractional Power Series Method (FPSM) is an effective and efficient method that offers an analytic method to find exact solution for Fractional Partial Differential Equations (FPDEs) in a functional space. In recent time, the FPSM has been applied in various science and engineering fields to solve physical problems in areas such as fluid dynamics, quantum mechanics, viscoelasticity, and heat conduction. This paper introduces a modification of the FPSM called the Fractional Gauss Hypergeometric Power Series Method (FGHPSM) which employs the so‐called Gauss Hypergeometric Function (GHF) to replace the Mittag–Leffler function in the FPSM on the grounds that the GHF generalizes the Mittag–Leffler function. This GHF when integrated into the FPSM provides not only exact solution but a generalized solution as compared with solution of the same equation using the FPSM. The FGHPSM is applied to solve fractional heat equation in two and three dimensions as well as fractional telegraph equation in a single dimension. The series obtained by the FGHPSM is derived to be in Sobolev spaces ensuring the existence of a unique solution. Also, a unique stable solution with respect to small perturbation in the initial conditions of the fractional heat and telegraph equations is established in this paper. MSC2020 Classification: 35J10

Suggested Citation

  • Isaac Addai & Benedict Barnes & Isaac Kwame Dontwi & Kwaku Forkuoh Darkwah, 2025. "Fractional Gauss Hypergeometric Power Series Method for Solving Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnlaaa:v:2025:y:2025:i:1:n:7650251
    DOI: 10.1155/aaa/7650251
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    References listed on IDEAS

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    1. Dumitru Baleanu & Praveen Agarwal, 2014. "On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
    2. Eleftherios Thalassinos & Naveed Khan & Shakeel Ahmed & Hassan Zada & Anjum Ihsan, 2023. "A Comparison of Competing Asset Pricing Models: Empirical Evidence from Pakistan," Risks, MDPI, vol. 11(4), pages 1-24, March.
    3. Dumitru Baleanu & Praveen Agarwal, 2014. "On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Khalid K. Ali & M. Maneea & Mohamed S. Mohamed & Yusuf Gurefe, 2023. "Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method," Journal of Mathematics, Hindawi, vol. 2023, pages 1-23, August.
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    1. Isaac Addai & Benedict Barnes & Isaac Kwame Dontwi & Kwaku Forkuoh Darkwah, 2025. "The Exact Solutions of the Fractional Partial Differential Equations Using the Fractional Prabhakar Power Series Method," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).

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