  We study the existence of global weak solutions of a nonlinear
transport-diffusion equation with a fractional derivative in the time variable
and under some extra hypotheses, we also study some regularity properties for
this type of solutions. In the system considered here, the diffusion operator
is given by a fractional Laplacian and the nonlinear drift is assumed to be
divergence free and it is assumed to satisfy some general stability and
boundedness properties in Lebesgue spaces.
