Exact Solutions And Analysis Of Two Classes Of Fractional Differential Equations

In recent decades,the theory of fractional order calculus equations has been applied to various fields and achieved many excellent results,fractional order differential equations also keep the momentum of further development in the context of various complex real-world problems,and in describing the dynamical behavior of some systems,fractional order differential equations are more able to reflect the actual change laws of the systems.In this paper,the exact solution problems of two types of fractional order FokasLenells equations are studied based on the theory of fractional order calculus equations.The main research contents and results are as follows:(1)Using the polynomial complete discriminant system method,nine exact solutions of this fractional-order Fokas-Lenells equation in the general case are obtained based on a complete classification of the single traveling wave solutions of a class of spacetime fractional-order Fokas-Lenells equations without any parameter restrictions,the relevant images of the exact solutions are plotted,and the influence of parameters on the structure of the solutions is thus analyzed;Based on the qualitative theory of differential equations,some new exact solutions of the equation are obtained by analyzing the qualitative nature of this equation,and the results are analyzed correspondingly.(2)Using the classical Lie group method,the exact solutions of a class of timefractional order Fokas-Lenells equations in one case are obtained,the conservation laws are obtained by proving the nature of nonlinear self-congruence of time-fractional order Fokas-Lenells equations,and the associated images of the exact solutions are plotted,and the influence of parameters on the structure of the solutions is also analyzed as a result.