A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation

Fatih Özbağ

doi:10.33187/jmsm.1838562

A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation

Abstract

This study introduces a novel two-dimensional fractional pseudo-telegraph equation that combines Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives—a hybrid approach not previously explored for this class of problems. A finite difference scheme is developed to solve the equation numerically. The stability of the proposed scheme is rigorously established through Von-Neumann analysis, yielding a sufficient stability condition. The convergence order of the method is shown to be $O(\tau^{2-\alpha}+h^2)$, where $\tau$ and $h$ denote the temporal and spatial step sizes, respectively. Numerical experiments are conducted for two test problems with known exact solutions. The computed maximum norm errors and CPU times, presented for various grid resolutions, demonstrate that the errors decrease monotonically as the mesh is refined, thereby confirming the accuracy and convergence of the method. The results validate that the proposed hybrid fractional model provides a reliable and efficient computational framework for handling mixed fractional-order derivatives in engineering and physical applications.

Keywords

Finite-difference method, Fractional derivative, Pseudo-telegraph equation

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Fatih Özbağ ^*
0000-0002-5456-4261
Türkiye

Early Pub Date

April 14, 2026

Publication Date

-

Submission Date

December 8, 2025

Acceptance Date

April 2, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.33187/jmsm.1838562

IZ

https://izlik.org/JA85YR82ZG

APA

Özbağ, F. (2026). A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation. Journal of Mathematical Sciences and Modelling, Advanced Online Publication, 85-93. https://doi.org/10.33187/jmsm.1838562

AMA

1.Özbağ F. A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation. Journal of Mathematical Sciences and Modelling. 2026;(Advanced Online Publication):85-93. doi:10.33187/jmsm.1838562

Chicago

Özbağ, Fatih. 2026. “A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation”. Journal of Mathematical Sciences and Modelling, no. Advanced Online Publication: 85-93. https://doi.org/10.33187/jmsm.1838562.

EndNote

Özbağ F (April 1, 2026) A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation. Journal of Mathematical Sciences and Modelling Advanced Online Publication 85–93.

IEEE

[1]F. Özbağ, “A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation”, Journal of Mathematical Sciences and Modelling, no. Advanced Online Publication, pp. 85–93, Apr. 2026, doi: 10.33187/jmsm.1838562.

ISNAD

Özbağ, Fatih. “A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation”. Journal of Mathematical Sciences and Modelling. Advanced Online Publication (April 1, 2026): 85-93. https://doi.org/10.33187/jmsm.1838562.

JAMA

1.Özbağ F. A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation. Journal of Mathematical Sciences and Modelling. 2026;:85–93.

MLA

Özbağ, Fatih. “A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation”. Journal of Mathematical Sciences and Modelling, no. Advanced Online Publication, Apr. 2026, pp. 85-93, doi:10.33187/jmsm.1838562.

Vancouver

1.Fatih Özbağ. A Hybrid Fractional Model Based on Caputo and Atangana–Baleanu–Caputo Derivatives for the 2D Pseudo-Telegraph Equation. Journal of Mathematical Sciences and Modelling. 2026 Apr. 1;(Advanced Online Publication):85-93. doi:10.33187/jmsm.1838562