Bifurcation, phase portrait and traveling wave solution of time-fractional thin-film ferroelectric material equation with beta fractional derivative

Abstract

In this paper, the bifurcation, phase portrait and traveling wave solution of time-fractional thin-film ferroelectric material equation with beta fractional derivative are studied, which are also the biggest innovations of this article compared with existing literature. Firstly, the time-fractional thin-film ferroelectric material equation with beta fractional derivative is converted into the nonlinear ordinary differential equation by using the traveling wave transformation. Secondly, the nonlinear ordinary differential equation is regarded as two-dimensional planar dynamical system. What's more, the bifurcation and phase portraits of two-dimensional planar dynamical system are plotted by using the Maple software. Finally, the traveling wave solutions of time-fractional thin-film ferroelectric material equation with beta fractional derivative are constructed by using the planar dynamical system method.