On the Solutions of the Space and Time Fractional Benjamin-Bona-Mahony Equation

In this paper, the extended trial equation method is used for constructing exact solutions of fractional partial differential equations (FPDEs) in the sense of Jumarie's modified Riemann-Liouville derivative. To convert a fractional partial differential equation into its ordinary differential equation of integer order is used the fractional complex transformation. With the aid of symbolic computation, we choose the space and time fractional Benjamin-Bona-Mahony (BBM) equation to illustrate the validity and advantages of this method. As a result, some new exact solutions including elliptic integral function solutions and soliton solutions to this problem are successfully established. The proposed approach can also be applied to other fractional partial differential equations (FPDEs).