This paper proposes a novel exponential rational function method, a modification of the well-known exp-function method, to find exact solutions of the time fractional Cahn-Allen equation and the time fractional Phi-4 equation. The solution procedure is reduced to solve a system of algebraic equations, which is then solved by Wu?s method. The results show that the present method is effective, and can be applied to other fractional differential equations.

Fractional Fokas equation is studied, its exact solution is obtained by the direct algebraic method. The solution process is elucidated step by step, and the fractional complex transform and the characteristic set algorithm are emphasized.

This paper applies the quasi hyperbolic function expansion method and the modified extended tanh-function method to exactly solve the nonlinear vibrating string equation and the elastic rod equation. The obtained exact solutions can be expressed by hyperbolic functions, which can outline various vibration properties.

This paper suggests a direct algebraic method for finding exact solutions of the space-time fractional (2+1)-dimensional breaking soliton equation. The solution procedure is reduced to solve a large system of algebraic equations, which is then solved by Wu?s method.

In this paper, some approximate analytical methods are reviewed, including the variational iteration method and the homotopy perturbation method. Based on the ideas of the two methods, a new method for solving a class of system of Fredholm integral equations of the second kind is proposed. Some examples are given to show the simple solution process and the accuracy of the solution for each method. The emphasis of this review paper focuses on Ji-Huan He?s unapproachable ideas and the mathematics beauty, so the references are not exhaustive.

In this paper, the direct construction method combined with the differential polynomial characteristic set algorithm is used to complete conservation laws of PDE. The process of the direct construction method is to solve a system of linear determining equations, which is not easy to be solved. This paper uses the differential polynomial characteristic set algorithm to overcome the shortcoming, and constructs an explicit conservation law.