Symmetries,Symmetry Reductions and Exact Solutions to the Generalized Nonlinear Fractional Wave Equations |
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| Authors: | Han-Ze Liu Zeng-Gui Wang Xiang-Peng Xin Xi-Qiang Liu |
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| Affiliation: | School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China |
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| 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. |
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| Keywords: | fractional differential equation Riemann-Liouville derivative Lie group classification Erdélyi-Kober fractional operator symmetry reduction exact solution |
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