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The doctoral thesis of the head of Department of Oil and Gas Management and Marketing at College of Industrial Management for Oil and Gas, Assistant Lecturer Mustafa Taha Yassin, was discussed on Thursday 10/31/2024 in the Department of Mathematics at College of Education for Pure Sciences (University of Basra) in the presence of the Dean of College of Industrial Management for Oil and Gas, Professor Dr. Sami Obaid Al-Tamimi.
The doctoral thesis was entitled "Branch Solutions for Some Nonlinear Fractional Differential Equations Using the Local Lyapunov-Schmidt Reduction Method." The thesis deals with investigating the bifurcation solutions for nonlinear fractional differential equations using one of the most important methods in modern mathematics, which is the Lyapunov-Schmidt method.
The study reviewed the examination and analysis of the bifurcation of periodic traveling wave solutions within a nonlinear fractional equation combine the derivative from fractional ordering techniques with Lyapunov-Schmidt reduction in our approach.
To simplify the analysis, the initial fractional equation which was differential transformed into a partial differential equation by using the fractional complex transformation. The transformation results in a condensed equation to be presented as a pair of nonlinear algebraic equations.
The researcher's investigation includes examining the linear approximation solutions of a nonlinear fractional differential equation. The researcher also discussed the bifurcation analysis of periodic traveling wave solutions of another nonlinear fractional differential equation and as a result, he arrived at obtaining a condensed equation which expressed as a system of four nonlinear algebraic equations that corresponds to the basic problem.
The researcher also investigated the possibility of finding linear approximate solutions to the nonlinear fractional differential equation. After a long and extensive discussion in the body of the thesis, the researcher received his doctorate degree amidst the joy of his colleagues and relatives.
