Variable separation method for a nonlinear time fractional partial differential equation with forcing term

In this paper, a variable-coefficient nonlinear time fractional partial differential equation (PDE) with initial and boundary conditions is solved by using the variable separation method. As a result, some new explicit and exact solutions of the time fractional PDE are obtained including Airy function solution, hyperbolic function solution, trigonometric function solution and rational solution. It is shown that the variable separation method can provide a useful mathematical tool for solving some other nonlinear time fractional PDEs in science and engineering.