An Investigation of the Bifurcation of Traveling Wave Solutions in Time-Fractional Nonlinear Differential Equations of the Symmetric Case - Yaseen, Mustafa T.; Hussain, Mudhir A. Abdul (Communications in Mathematics and Applications, 2025)
This study considers examining and bifurcation of traveling wave solutions in time-fractional nonlinear differential equations of the symmetric case. We blend Li and He’s derivative of fractional order techniques with Lyapunov-Schmidt reduction in our approach. To simplify the analysis, the initial fractional equation that is differential is transformed into a partial differential equation through the utilization of the fractional complex transform. This conversion results in a condensed equation, presented as a pair of nonlinear algebraic equations, tackling the core issue. Furthermore, our investigation involves examining linear approximation solutions for a nonlinear fractional equation (NFE) that is differential.