AN IMPLICIT DIFFERENCE METHOD FOR SOLVING COUPLED MOBILE/IMMOBILE TRANSPORT SYSTEMS WITH GENERALIZED TIME-FRACTIONAL OPERATORS

Shengda Zeng (), Jinsheng Du () and Sergey A. Timoshin
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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

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-17

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.

Keywords: Mobile/Immobile Transport Equations; Coupled System; Implicit Difference Scheme; Caputo–Katugampola Fractional Operator; L1 Discretization Formula; Stability and Convergence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400857

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