Symmetries, Symmetry Reductions and Exact Solutions to the Generalized Nonlinear Fractional Wave Equations**Supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, the Natural Science Foundation of Shandong Province under Grant No. ZR2015AL008, and the High-Level Personnel Foundation of Liaocheng University under Grant No. 31805

Abstract

In this paper, the Lie group classification method is performed on the fractional partial differential equation (FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations (FODEs) in terms of the Erdélyi-Kober (E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.