Abstract
The present study is devoted to investigate the (2+1)-dimensional time-fractional long-wave dispersive (fLWD) model, which describes the dynamical behaviors of shallow water waves propagate along two horizontal directions with fast memories. We first establish the symmetries and conservation laws for this model by improving the fractional Lie group approach and fractional Noether’s formulae. Then, using the general fractional Erdelyi–Kober operator, we reduce the original equations into a time-fractional integro-differential system. Finally, the invariant subspace method is applied to this model to obtain more explicit solutions and the dynamical behaviors are analyzed through numerical simulations. This work extends the basic method to solve the higher dimensional system with mixed order of integer and fractional derivatives.
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