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Numerical simulation and error analysis for a novel fractal–fractional reaction diffusion model with weighted reaction

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  • Zhang, Lihong
  • Lu, Keke
  • Ahmad, Bashir

Abstract

A new fractal-fractional reaction diffusion model with weighted reaction is investigated in this paper. Using Chelyshkov polynomials, we construct the associated Chelyshkov operator matrix to solve this diffusion model. An error estimation is obtained for validation of our method. Numerical examples indicate that the proposed method is easy to apply and produce accurate results. It is imperative to mention that the fractal-fractional reaction diffusion model and the proposed numerical method offer an efficient approach to handle the issues related to the diffusion phenomenon.

Suggested Citation

  • Zhang, Lihong & Lu, Keke & Ahmad, Bashir, 2025. "Numerical simulation and error analysis for a novel fractal–fractional reaction diffusion model with weighted reaction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 227-240.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:227-240
    DOI: 10.1016/j.matcom.2024.11.013
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    1. Jeongjun Park & Gigwon Hong, 2022. "Simulation on the Permeability Evaluation of a Hybrid Liner for the Prevention of Contaminant Diffusion in Soils Contaminated with Total Petroleum Hydrocarbon," IJERPH, MDPI, vol. 19(20), pages 1-17, October.
    2. Hsiao, Chun-Hui, 2004. "Haar wavelet direct method for solving variational problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 569-585.
    3. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    4. Tu, Yunbo & Meng, Xinzhu, 2023. "A reaction–diffusion epidemic model with virus mutation and media coverage: Theoretical analysis and numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 28-67.
    5. Ali H. Bhrawy & Mahmoud A. Zaky & José A. Tenreiro Machado, 2017. "Numerical Solution of the Two-Sided Space–Time Fractional Telegraph Equation Via Chebyshev Tau Approximation," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 321-341, July.
    6. Salman Jahanshahi & Delfim F. M. Torres, 2017. "A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 156-175, July.
    7. Shloof, A.M. & Senu, N. & Ahmadian, A. & Salahshour, Soheil, 2021. "An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 415-435.
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