The College of Education for Pure Sciences discussed a doctoral thesis on
(Branch solutions for some nonlinear fractional differential equations using the local Lyapunov-Schmidt reduction method)
The thesis presented by the researcher (Mustafa Taha Yassin)
This study included examining and analyzing the bifurcation of periodic traveling wave solutions within a nonlinear fractional equation. We combine the derivative He of fractional ordering 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 by using the fractional complex transformation. This transformation results in a condensed equation, which is presented as a pair of nonlinear algebraic equations. Our investigation includes examining the linear approximation solutions of a nonlinear fractional differential equation. We also studied the bifurcation analysis of periodic traveling wave solutions for another nonlinear fractional differential equation. As a result, we obtain a reduced equation, which is expressed as a system of four nonlinear algebraic equations that correspond to the basic problem. We also discuss the possibility of finding linear approximate solutions to a nonlinear fractional differential equation.
