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Fractional Analysis Of Population Dynamical Model In (3+1)-Dimensions With Fractal-Fractional Derivatives

Author

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  • FENGLIAN LIU

    (Institute of Land & Resources and Sustainable Development, Yunnan University of Finance and Economics, Kunming 650221, P. R. China)

  • BOWEN YANG

    (Institute of Land & Resources and Sustainable Development, Yunnan University of Finance and Economics, Kunming 650221, P. R. China)

  • LI ZHANG

    (��Suan Sunandha Rajabhat University, Bangkok 10300, Thailand‡School of International Language and Culture, Yunnan University of Finance and Economics, Kunming 650221, P. R. China)

  • MUHAMMAD NADEEM

    (�School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China)

  • NAIF ALMAKAYEEL

    (�Department of Industrial Engineering, College of Engineering, King Khalid University, Abha, Saudi Arabia)

  • MESHAL SHUTAYWI

    (��Department of Mathematics, College of Science & Arts, King Abdul Aziz University, Rabigh, Saudi Arabia)

Abstract

The fractal-fractional derivative is a powerful tool that is generally used for the mathematical analysis of complex and unpredictable structures. In this paper, we study a population dynamical model of (3+1)-dimensional form using the fractal derivative involving fractional order with power law kernel. The proposed scheme is known as the Sumudu Homotopy Transform Method (ð •ŠHTM), which depends on the association between the Sumudu Transform (ð •ŠT) and the Homotopy Perturbation Method (HPM). The convergence of the derived results is verified by comparing the errors in consecutive iterations with the ð •ŠHTM results. We display the behavior of the obtained results in three-dimensional shape across the various orders of fractal and fractional derivatives. We present three numerical tests to validate the accuracy of ð •ŠHTM and compare the acquired findings to the exact outcomes of the suggested model. This analysis confirms that the ð •ŠHTM results align perfectly with the accurate results. As a result, the ð •ŠHTM is widely recognized as a leading computational method for obtaining approximate solutions to various nonlinear complex fractal-fractional problems.

Suggested Citation

  • Fenglian Liu & Bowen Yang & Li Zhang & Muhammad Nadeem & Naif Almakayeel & Meshal Shutaywi, 2025. "Fractional Analysis Of Population Dynamical Model In (3+1)-Dimensions With Fractal-Fractional Derivatives," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:03:n:s0218348x24501275
    DOI: 10.1142/S0218348X24501275
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