  We prove that any given function can be smoothly approximated by functions
lying in the kernel of a linear operator involving at least one fractional
component. The setting in which we work is very general, since it takes into
account anomalous diffusion, with possible fractional components in both space
and time. The operators studied comprise the case of the sum of classical and
fractional Laplacians, possibly of different orders, in the space variables,
and classical or fractional derivatives in the time variables.
  This type of approximation results shows that space-fractional and
time-fractional equations exhibit a variety of solutions which is much richer
and more abundant than in the case of classical diffusion.
