The Traveling Wave Solutions For Two Classes Of Fractional Differential Equations

In this paper,we apply Feng's first integral method to study the solution of space-time fractional Whitham-Broer-Kaup(WBK)type equation and space-time fractional Symmetric Regularized Long Wave(SRLW)equation where 0<? ? 1,?,?,? are constents.As a result,solitary wave solution,hyperbolic function solution,trigonometric function solution and other exact solutions are obtained.First integral method has the advantages of convenient application and quick calcula-tion,so as to avoid a lot of complicated and tedious calculation,but also can obtain accurate and explicit travelling wave solutions.So,in recent years,the high attention by physical and applied mathematicians has been applied to many mathematical physics model of the problem including fractional order differential equation.The first chapter mainly introduces the research background of fractional order differ-ential equations and its solutions.The second chapter briefly introduces several kinds of definitions,properties of fractional derivative and the fractional order differential equation solving method of travelling wave solutions.The third chapter will apply the method in the second chapter to the two types of fractional differential equations,and to get the main result of this paper.