FRACTIONAL ANALYSIS OF POPULATION DYNAMICAL MODEL IN (3+1)-DIMENSIONS WITH FRACTAL-FRACTIONAL DERIVATIVES

Fenglian Liu, Bowen Yang, Li Zhang, Muhammad Nadeem, Naif Almakayeel and Meshal Shutaywi
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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

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-16

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.

Keywords: Sumudu Homotopy Transform Method; Power Law Kernel; Convergence Analysis; Fractal-Fractional Model; Approximate Solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501275

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