linear and nonlinear fractional differential equation modified Riemann–Liouville derivatives exact solutions fractional auxiliary sub-equation expansion method Mittag–Leffler function method  

作　　者：Emad A-B.Abdel-Salam Gamal F.Hassan 

机构地区：Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, E1-Kharja 72511, Egypt

出　　处：《Communications in Theoretical Physics》2016年第2期127-135,共9页理论物理通讯（英文版）

摘　　要：In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Kd V equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the（3＋1）-spacetime fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag–Leffler function methods. The obtained results recover the well-know solutions when α = 1.

关 键 词：Solutions to Class of Linear and Nonlinear Fractional Differential Equations 

分 类 号：O175.14[理学—数学] TP391.9[理学—基础数学]