Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations

In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie’s modified Riemann–Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada–Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed.