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A Novel Approach to Solving Fractional-Order Kolmogorov and Rosenau–Hyman Models through the q-Homotopy Analysis Transform Method

Author

Listed:
  • Laila F. Seddek

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
    Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt)

  • Essam R. El-Zahar

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt)

  • Jae Dong Chung

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea)

  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea)

Abstract

In this study, a novel method called the q-homotopy analysis transform method (q-HATM) is proposed for solving fractional-order Kolmogorov and Rosenau–Hyman models numerically. The proposed method is shown to have fast convergence and is demonstrated using test examples. The validity of the proposed method is confirmed through graphical representation of the obtained results, which also highlights the ability of the method to modify the solution’s convergence zone. The q-HATM is an efficient scheme for solving nonlinear physical models with a series solution in a considerable admissible domain. The results indicate that the proposed approach is simple, effective, and applicable to a wide range of physical models.

Suggested Citation

  • Laila F. Seddek & Essam R. El-Zahar & Jae Dong Chung & Nehad Ali Shah, 2023. "A Novel Approach to Solving Fractional-Order Kolmogorov and Rosenau–Hyman Models through the q-Homotopy Analysis Transform Method," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1321-:d:1092158
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    References listed on IDEAS

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    1. Alexander Sukhinov & Alexander Chistyakov & Elena Timofeeva & Alla Nikitina & Yulia Belova, 2022. "The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation," Mathematics, MDPI, vol. 10(16), pages 1-15, August.
    2. Mohammed Al-Smadi & Omar Abu Arqub & Shaher Momani, 2013. "A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-10, April.
    3. Alexander Sukhinov & Alexander Chistyakov & Inna Kuznetsova & Yulia Belova & Elena Rahimbaeva, 2022. "Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems," Mathematics, MDPI, vol. 10(19), pages 1-21, September.
    4. Hasan, Shatha & El-Ajou, Ahmad & Hadid, Samir & Al-Smadi, Mohammed & Momani, Shaher, 2020. "Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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