A New Approach for Solving Fractional Partial Differential Equations in the Sense of the Modified Riemann-Liouville Derivative

Based on a fractional complex transformation, certain fractional partial differential equation in the sense of the modified Riemann-Liouville derivative is converted into another ordinary differential equation of integer order, and the exact solutions of the latter are assumed to be expressed in a polynomial in Jacobi elliptic functions including the Jacobi sine function, the Jacobi cosine function, and the Jacobi elliptic function of the third kind. The degree of the polynomial can be determined by the homogeneous balance principle. With the aid of mathematical software, a series of exact solutions for the fractional partial differential equation can be found. For demonstrating the validity of this approach, we apply it to solve the space fractional KdV equation and the space-time fractional Fokas equation. As a result, some Jacobi elliptic functions solutions for the two equations are obtained.