The Exact Solutions Of Several Time Fractional Nonlinear Partial Differential Equations

The nonlinear partial differential equation has become a hot topic in the field of nonlinear science,and is used to describe the problems in many fields,such as quantum mechanics,image processing,ecology and economic system,epidemiology,etc.However,for some complex problems in these fields,fractional nonlinear partial differential equation is more accurate than integer nonlinear partial differential equation,so obtain the exact solutions of the fractional nonlinear partial differential equation becomes extremely important.In recent years,many scholars have studied the exact solutions of the fractional nonlinear partial differential equation,which has effectively promoted the development of the field of nonlinear partial differential equation.The main contents of this thesis are divided into the following parts:Firstly,we introduce the origin and development of fractional calculus,and then give the definition and properties of conformable fractional derivative.Secondly,based on conformable fractional derivative and traveling wave transformation,we give the solutions of some hyperbolic functions for the nonlinear generalized time fractional Sharma-Tasso-Olver equation and Zakharov equations by using the generalized Kudryashov method.With Maple,the corresponding intuitive 3D graph of each solution under the specified parameters is obtained.In addition,combining with conformable fractional derivative,we introduce the basic idea and concrete steps of the invariant subspace method.And the validity of this method in obtaining the exact solutions of the fractional nonlinear dispersion equations and the fractional Boussinesq equations is verified.Finally,the thesis is summarized,and put forward for the future research work.