Traveling wave solutions for fractional partial differential equations arising in mathematical physics by an improved fractional Jacobi elliptic equation method

In this paper, combining with a new generalized ansätz and the fractional Jacobi elliptic equation, an improved fractional Jacobi elliptic equation method is proposed for seeking exact solutions of space‐time fractional partial differential equations. The fractional derivative used here is the modified Riemann‐Liouville derivative. For illustrating the validity of this method, we apply it to solve the space‐time fractional Fokas equation and the the space‐time fractional BBM equation. As a result, some new general exact solutions expressed in various forms including the solitary wave solutions, the periodic wave solutions, and Jacobi elliptic functions solutions for the two equations are found with the aid of mathematical software Maple.