Exact Solutions To A Class Of Fractional Nonlinear Partial Differential Equations

The fractional order differential equations are often used to establish mathematical models in the application fields such as signal processing,vibration and control of the robots,optics,thermology and so on.However,few research projects have been carried out to solve the exact solutions of fractional order differential equations.And what's more,so far,there is no uniform method to solve this problem.Therefore,it is of great significance to study the properties,the basic theory and the computing method of fractional differential equations.This paper mainly introduces the Riemann-Liouville derivative,and the improved exp(-?(?))-expansion method and the improved F-expansion method.Both methods are used to find exact traveling wave solutions to the fractional KdV equation,fractional(2+1)-dimensional breaking soliton equations,the space-time fractional BBM equation and the space-time fractional order Quadratic Klein-Gordon equation.In the process of solving these equations,the modified Riemann-Liouville derivative is applied to convert the fractional nonlinear partial differential equations to nonlinear ordinary differential equations at first.Then according to the balance principle,the exact traveling wave solutions to the fractional nonlinear different equations are constructed by using Mathematica software.Finally,the 3D graphs of the corresponding solutions to the above fractional nonlinear differential equations are also given.The results further illustrate the applicability and superiority of the above two methods for solving a class of fractional nonlinear evolution.