  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.
