The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations

An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansatz and Backlund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers' equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.