  We investigate the existence of exact solutions in closed form to a
fractional version of the nonlinear Boussinesq equation for groundwater flow
through an unconfined aquifer. We show this fractional equation appears
naturally when the classical nonlinear Darcy's law is replaced by a
space-fractional one. After a physical discussion on the fractional model, we
give several exact solutions in closed form for special choices of initial and
boundary data. We provide solutions for steady and unsteady cases, by
considering both classical and fractional derivatives in time.
