  We consider an anisotropic L\'evy operator $\mathcal{I}_s$ of any order
$s\in(0,1)$ and we consider the homogenization properties of an evolution
equation.
  The scaling properties and the effective Hamiltonian that we obtain is
different according to the cases $s<1/2$ and $s>1/2$.
  In the isotropic onedimensional case, we also prove a statement related to
the so-called Orowan's law, that is an appropriate scaling of the effective
Hamiltonian presents a linear behavior.
