Numerical Solutions for Mixed Fractional Order Two-Dimensional Telegraph Equations

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.