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Peer-reviewedCC BY 4.0Fractal and Fractional

A Numerical Analysis for Solving the Time-Fractional Cattaneo Model Involving the Riesz Space-Fractional Derivative

  • Mousa J. Huntul1
  • Abdullah A. Zaagan1
  1. 1Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia
Open at sourceDOICite

Abstract

This manuscript presents an efficient hybrid numerical method for solving one- and two-dimensional time-fractional Cattaneo models that incorporate the Riesz space-fractional derivative. The proposed approach combines the Crank–Nicolson scheme for temporal discretization with the classical Galerkin finite element method for spatial discretization. The stability of the semi-discrete scheme is established in the L2 norm, and a convergence analysis of the fully discrete scheme is carried out, yielding a temporal convergence order of O(Δt)3−μ and a spatial convergence order of O(R2). Finally, two numerical examples, in one and two dimensions, are provided to demonstrate the accuracy and efficiency of the proposed method and to verify the theoretical findings.

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Cite

BibTeXRIS
BibTeX
@article{huntul2026numerical,
  title = {{A Numerical Analysis for Solving the Time-Fractional Cattaneo Model Involving the Riesz Space-Fractional Derivative}},
  author = {Mousa J. Huntul and Abdullah A. Zaagan},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10100710},
  url = {https://www.mdpi.com/2504-3110/10/10/710},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Numerical Analysis for Solving the Time-Fractional Cattaneo Model Involving the Riesz Space-Fractional Derivative
AU  - Mousa J. Huntul
AU  - Abdullah A. Zaagan
PY  - 2026
DA  - 2026/10/09
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10100710
UR  - https://www.mdpi.com/2504-3110/10/10/710
AB  - This manuscript presents an efficient hybrid numerical method for solving one- and two-dimensional time-fractional Cattaneo models that incorporate the Riesz space-fractional derivative. The proposed approach combines the Crank–Nicolson scheme for temporal discretization with the classical Galerkin finite element method for spatial discretization. The stability of the semi-discrete scheme is established in the L2 norm, and a convergence analysis of the fully discrete scheme is carried out, yielding a temporal convergence order of O(Δt)3−μ and a spatial convergence order of O(R2). Finally, two numerical examples, in one and two dimensions, are provided to demonstrate the accuracy and efficiency of the proposed method and to verify the theoretical findings.
SN  - 2504-3110
ER  -