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Lyapunov-Schmidt reduction in the study of bifurcation solutions of nonlinear fractional differential equation. (English) Zbl 1415.35031
Summary: In this article the bifurcation of periodic travelling wave solutions of nonlinear fractional differential equation is studied by using Lyapunov-Schmidt reduction and He’s fractional derivative. The fractional complex transform is used to convert the fractional differential equation into partial differential equation. The reduced equation corresponding to the main problem is found as a system of two nonlinear algebraic equations. The existence of the linear approximation solutions of the nonlinear fractional differential equation is discussed.
MSC:
35B32 Bifurcations in context of PDEs
35R11 Fractional partial differential equations
35C07 Traveling wave solutions
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