  The fractional Fokker-Planck equation, which contains a variable diffusion
coefficient, is discussed and solved. It corresponds to the L\'evy flights in a
nonhomogeneous medium. For the case with the linear drift, the solution is
stationary in the long-time limit and it represents the L\'evy process with a
simple scaling. The solution for the drift term in the form
$\lambda\hbox{sgn}(x)$ possesses two different scales which correspond to the
L\'evy indexes $\mu$ and $\mu+1$ $(\mu<1)$. The former component of the
solution prevails at large distances but it diminishes with time for a given
$x$. The fractional moments, as a function of time, are calculated. They rise
with time and the rate of this growth increases with $\lambda$.
