Fractional Sub-equation Method and Analytical Solutions to the Hirota-satsuma Coupled KdV Equation and Coupled mKdV Equation

The fractional sub-equation method is proposed to construct analytical solutions of nonlinear fractional partial differential equations (FPDEs), involving Jumarie’s modified Riemann-Liouville derivative. The fractional sub-equation method is applied to the space-time fractional generalized Hirota-Satsuma coupled KdV equation and coupled mKdV equation. The analytical solutions show that the fractional sub-equation method is very effective for the fractional coupled KdV and mKdV equations. The solutions are compared with that of the extended tanh-function method. New exact solutions are found for the coupled mKdV equation.