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An Implicit Difference Method For Solving Coupled Mobile/Immobile Transport Systems With Generalized Time-Fractional Operators

Author

Listed:
  • SHENGDA ZENG

    (Center for Applied Mathematics of Guangxi, Guangxi Colleges and Universities Key Laboratory of Complex, System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, People’s Republic of China)

  • JINSHENG DU

    (College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China)

  • SERGEY A. TIMOSHIN

    (School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, P. R. China4Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Lermontov Street 134, 664033 Irkutsk, Russia)

Abstract

This paper introduces an implicit difference scheme for solving a specific class of coupled mobile/immobile transport systems involving generalized time-fractional operators, in which we discretize the derivative with respect to time using the first-order backward difference method. To handle the generalized fractional-order derivative, we employ the L1 discretization formula. We approximate the spatial derivative with the help of the formula for the central difference method. The main contribution of this paper is two-fold. First, the energy method is applied to establish the convergence and stability of an implicit difference scheme under the L∞ norm. Second, we study two examples and provide numerical results to demonstrate the effectiveness of theoretical results we obtained.

Suggested Citation

  • Shengda Zeng & Jinsheng Du & Sergey A. Timoshin, 2025. "An Implicit Difference Method For Solving Coupled Mobile/Immobile Transport Systems With Generalized Time-Fractional Operators," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-17.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:04:n:s0218348x25400857
    DOI: 10.1142/S0218348X25400857
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    More about this item

    Keywords

    Mobile/Immobile Transport Equations; Coupled System; Implicit Difference Scheme; Caputo–Katugampola Fractional Operator; L1 Discretization Formula; Stability and Convergence;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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