  We consider different generalizations of the Fokker-Planck-equation devised
to describe Levy processes in potential force fields. We show that such
generalizations can proceed along different lines. On one hand,
  Levy statistics can emerge from the fractal temporal nature of the underlying
process, i.e. a high variability in the rate of microscopic events. On the
other hand, they may be a direct consequence of the scale-free spatial
structure on which the process evolves. Although both forms considered lead to
Boltzmann equilibrium, the relaxation patterns are quite different.
  As an example, generalized diffusion in a double-well potential is
considered.
