The double auxiliary equations method and its application to space-time fractional nonlinear equations

Abstract

This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation. The proposed scheme has been successfully applied on two very important evolution equations, the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation. The obtained results show that the proposed method is more powerful, promising and convenient for solving nonlinear fractional differential equations (NFPDEs). To our knowledge, the solutions obtained by the proposed method have not been reported in former literature. Keywords: Double auxiliary equations method, Fractional partial differential equation, Exact solution, Traveling wave solution, Nonlinear low-pass electrical Transmission lines, Fractional Burger’s equation