Fractional Sub-Equation Method and its Applications to the Space–Time Fractional Differential Equations in Mathematical Physics

In the present paper, we construct the analytical solutions of some nonlinear evolution equations involving Jumarie’s modified Riemann–Liouville derivative in mathematical physics; namely the space–time fractional modified Benjamin-Bona-Mahony(mBBM) equation and the space–time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony(ZKBBM) equation by using a simple method which is called the fractional sub-equation method. As a result, three types of exact analytical solutions are obtained. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear fractional PDEs arising in mathematical physics.