Method of separating variables combined with approach of dynamic system for investigating exact solutions of nonlinear time‐fractional models

Abstract

In this paper, we introduce a combination method called method of separating variables and approach of dynamic system. As an application example, by using this combination method, we study two nonlinear time‐fractional models called time‐fractional reaction–diffusion equations. Under different parametric regions, phase portraits of the systems which are derived from the parts of space variables of the two reaction–diffusion equations are given. In free boundary conditions, the existence of solution of the two nonlinear time‐fractional models is studied. In some special parametric conditions, some exact solutions of the two time‐fractional models are obtained. Dynamic phenomena of some representative exact solutions developing with time and space variables are illustrated by 3D graphs of numerical simulation.