Nonlinear time-fractional dispersive equations

In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method.This method allows to find exact solutions to nonlinear time-fractional partial differential equations by separating variables.We first consider a third order time-fractional NDE that admits a four-dimensional invariant subspace and we find a similarity solution.We also study a fifth order NDE.In this last case we find a solution involving Mittag-Leffler functions.We finally observe that the invariant subspace method permits to find explicit solutions for a wide class of nonlinear dispersive time-fractional equations.