Abstract
The main purpose of this paper is to study the dynamical behavior, optical soliton solution and traveling wave solution for the fractional Biswas-Arshed equation with the beta time derivative by using theory of planar dynamical system. Firstly, by employing the traveling wave transformation and other integral transformations, the fractional Biswas-Arshed equation with the beta time derivative is simplified into two-dimensional planar dynamic system. Secondly, phase portraits for the fractional Biswas-Arshed equation with the beta time derivative are plotted. Finally, based on Professor Li's three-step method, optical soliton solution and traveling wave solution of the fractional Biswas-Arshed equation with the beta time derivative are constructed, the obtained solutions give the propagation of optical solitons in nonlinear optics.
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