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

Author

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  • Ateq Alsaadi
  • Ramsha Shafqat
  • Abeer M. Alsaadi

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.

Suggested Citation

  • Ateq Alsaadi & Ramsha Shafqat & Abeer M. Alsaadi, 2026. "An M-Matrix-Based Finite Difference Framework for Atangana–Baleanu–Caputo Fractional Diffusion Equations With Nonsingular Memory," Journal of Mathematics, Hindawi, vol. 2026, pages 1-12, August.
    • Handle: RePEc:hin:jjmath:4588551
    DOI: 10.1155/jom/4588551
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