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A stable and convergent fully discrete scheme for solving two-dimensional distributed-order fractional cable models | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 3، آبان 2026، صفحه 891-907 اصل مقاله (579.59 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.32479.2945 | ||
| نویسندگان | ||
| Hamid Rezaei* 1؛ Meysam Asadipour2؛ Mohammad Hossein Derakhshan2 | ||
| 1Department of Mathematics, College of Sciences, Yasouj University, Yasouj-, 75914-74831, Iran | ||
| 2Department of Mathematics, College of Sciences, Yasouj University, Yasouj-75914-74831, Iran | ||
| چکیده | ||
| This paper investigates a novel distributed-order time-fractional cable equation involving both Caputo and Riemann– Liouville fractional derivatives, which models complex diffusion and memory effects in various physical and biological systems. The proposed model incorporates a distributed-order fractional Laplacian term, a memory integral, and a nonlinear source, capturing multiscale temporal dynamics and nonlocal behavior. A robust numerical scheme is developed by applying a fractional Adams–Bashforth–Moulton predictor-corrector method for time discretization, while central difference approximations are used for the spatial Laplacian. This results in a fully discrete scheme that effectively combines the advantages of convolution quadrature with classical finite difference methods. A detailed convergence and stability analysis of the numerical method is presented using an energy-based approach and a discrete fractional Gronwall inequality. The method is proven to be unconditionally stable and achieves optimal convergence rates in both time and space. Numerical simulations confirm the theoretical predictions and demonstrate the accuracy and efficiency of the scheme in capturing the underlying fractional dynamics. The proposed framework offers a powerful and flexible tool for the numerical simulation of fractional-order systems with distributed memory, and can be extended to a wide range of multi-term and distributed-order fractional partial differential equations. | ||
| کلیدواژهها | ||
| Distributed-order fractional differential equations؛ cable equation؛ fractional Adams--Bashforth--Moulton method؛ stability analysis؛ numerical simulation | ||
| مراجع | ||
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