An investigation of the bifurcation of traveling wave solutions in time-fractional nonlinear differential equations of the symmetric case - Yaseen, Mustafa Taha; Abdul Hussain, Mudhir A. (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 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.