The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics ✩

Abstract By introducing a new general ansatz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarieʼs modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations.