In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.

In this paper, a sixth-order parabolic thin film equation with the initial boundary condition is considered. By using the improved energy estimate method and by constructing second-order elliptic problem, a blow-up result for certain solution with positive initial energy is established, which is an improve over the previous result of Li and Liu.