Bifurcation Analysis And Solutions Structure Of Three Nonlinear Fractional Partial Differential Equations

In this paper,we analyze and construct bifurcation and solution-s of the nonlinear space-time fractional Telegraph equation,(4+1)dimensional space-time fractional Fokas equation,(2+1)dimensional time fractional order ZK-MEW equation.The process and results of the method are as follows:Combining with the integrated fractional dervative,using the extended(G’/G)-expansion method,and introducing a new auxiliary equation,the exact solutions of nonlinear space-time fractional Telegraph equation are constructed.The new exact solutions contain trigonometric function solution,hyperbolic function solu-tion and rational function solution.By integrating fractional derivatives and using the bifurcation theory of dy-namic systems,the nonlinear partial differential equation is transformed into a plane dynamic system.Using maple software to draw the plane phase diagram of the equation.Then,the exact travelling wave solutions of the original equa-tion have been constructed according to the trajectory of the phase diagram.These solutions include periodic wave solutions,periodic singular wave solutions,blasting wave solutions and solitary wave solutions.