Two Methods For The Exact Solutions Of Fractional Partial Differential Equations

In recent years,the fractional differential equations have been applied in a wide range of fields,including biotechnology,high energy physics,system control,anomalous diffusion and so on.Nevertheless,there is no uniform approach in regard of solving the fractional differential equations until now.Therefore,searching for the solutions to the fractional differential equations has become a hot research area.In this paper,the related concepts of the fractional calculus are introduced,and the theories of fractional calculus based on the definition of modified Riemann-Liouville derivatives are applied to find the solutions of fractional differential equations.The generalized exp(-?(?))-expansion method has been improved and the fractional Sharma-Tassso-Olever(STO)equation,fractional Cahn-Allen(CA)equation and fractional Whitham-Broer-Kaup(WBK)equations are solved by this method and the first integral method respectively in this paper.As a result,the exact solutions to the above equations are obtained in forms of the trigonometric,hyperbolic,rational and exponential functions.The validity and simplicity of these two methods to find exact solutions of the fractional differential equations are well illustrated by the given examples.