Group classification, symmetry reductions and exact solutions of the time-fractional generalized thin film equation with variable coefficients

In this paper, we investigate the time-fractional generalized thin film equation (TFGTFE) with two arbitrary functions and perform the group classification with respect to these arbitrary functions. Specifically, all vector fields admitted by the considered equations are provided utilizing Lie symmetry analysis. Then the corresponding symmetry reductions are carried out and exact solutions to some special equations are obtained. In particular, we construct the power series solutions to one type of TFGTFE by means of the combination of the Erdelyi-Kober (EK) operator with the analytic power series method and verify the convergence of the power series solutions using implicit function theorem. In addition, taking advantage of Matlab software, the three-dimensional diagrams and two-dimensional graphs of some obtained solutions are demonstrated for the purpose of visualization.