Exact solutions and dynamic properties of a nonlinear fourth-order time-fractional partial differential equation

Abstract

This paper considers a fourth-order time-fractional partial differential equation with Riemann–Liouville definition. We first use the general method of separation of variables to transform the original equation into an ordinary differential equation and subsequently apply the trial equation method to obtain its integral form. The complete discrimination system for polynomial method(CDSPM) is also adopted herein. By applying this method, dynamic properties such as phase portraits are determined. The results suggest that the soliton solution coexists with the periodic solution as long as the homoclinic orbits exist. Moreover, to directly show our conclusions, the corresponding exact solutions to this equation are presented using this method.