Numerical Solutions for Mixed Fractional Order Two-Dimensional Telegraph Equations

Year 2024, Volume: 13 Issue: 4, 1023 - 1030, 31.12.2024

Fatih Özbağ , Mahmut Modanlı , Sadeq Taha Abdulazeez

https://doi.org/10.17798/bitlisfen.1495657

Abstract

This research presents an innovative numerical approach to solving two-dimensional telegraph equations of mixed fractional order by integrating the fractional derivatives of Caputo and Atangana-Baleanu Caputo (ABC) into a single model. Using MATLAB as its implementation, the research creates a customized first-order difference scheme and analyses stability. The ability to manage mixed fractional derivatives in 2D telegraph equations, a situation that has not been tackled in literature before, is the method's innovative aspect. This development shows that these complicated equations may be efficiently and reliably modelled, opening up new avenues for the study of complex physical phenomena. The work makes a substantial contribution to the numerical analysis of fractional differential equations with mixed derivative types and opens up possible applications in areas like wave propagation and anomalous diffusion processes.

Keywords

Two-Dimensional Telegraph Equation, Caputo and ABC Fractional Derivatives, Finite Difference Technique, Numerical Solution

Ethical Statement

The study is complied with research and publication ethics

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