Exact Solutions For Two Classes Of Nonlinear Fractional Partial Differential Equations

In this thesis,we study exact solutions of two classes of nonlinear fractional partial differential equations.Firstly,a class of space-time fractional mixed(1+1)-dimensional KdV equations are considered.The nonlinear fractional partial differential equations are transformed into nonlinear ordinary differential equations of integer order by means of fractional complex transformations,by applying the first integral method and Maple software,and we obtain the exact solutions and figures.Then,a class of time fractional coupled Boussinesq–Burger equations are studied by using the invariant subspace method.In the sense of variable transformation,and the invariant subspace of the coupled equations is given by invariant conditions,and the coupled equations are reduced to ordinary differential equations in the invariant subspace.Finally,by solving ordinary differential equations,the exact solutions are obtained.This paper is organized as follows:In the first chapter,we introduce the research progress of fractional partial differential equations,the properties of fractional derivatives,the research backgrounds of two classes of equations,and the main work of this paper.In the second chapter,with the conclusion of the Riccati equation,the hyperbolic function solution,rational function solution and traveling wave solution of the space-time fractional mixed(1+1)-dimensional KdV equations are obtained by applying the first integral method,and figures are drawed by Maple software.In the third chapter,a class of time fractional coupled Boussinesq–Burger equations are studied by using the invariant subspace method,and the exact solutions of the integer and fractional order are obtained.In the fourth chapter,we conclude the works in our paper and give some further consideration on our next research.