An M-Matrix-Based Finite Difference Framework for Atangana–Baleanu–Caputo Fractional Diffusion Equations With Nonsingular Memory

Ateq Alsaadi, Ramsha Shafqat and Abeer M. Alsaadi

Journal of Mathematics, 2026, vol. 2026, 1-12

Abstract: We develop a finite difference method for time-fractional diffusion equations involving the Atangana–Baleanu–Caputo (ABC) derivative with a nonsingular Mittag–Leffler kernel. The temporal derivative is approximated by an ABC-adapted L1-type formula, while the spatial derivative is discretized by a second-order central difference scheme. The resulting fully discrete system is analyzed using the positivity and monotonicity of the ABC memory weights together with an M-matrix argument. The scheme is shown to be unconditionally stable and convergent with accuracy Oτ2−α+h2. Numerical experiments confirm the theoretical convergence behavior and illustrate the effect of the fractional order on the diffusion dynamics.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4588551

DOI: 10.1155/jom/4588551

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