  We are concerned with the long time behaviour of solutions to the fractional
porous medium equation with a variable spatial density. We prove that if the
density decays slowly at infinity, then the solution approaches the
Barenblatt-type solution of a proper singular fractional problem. If, on the
contrary, the density decays rapidly at infinity, we show that the minimal
solution multiplied by a suitable power of the time variable converges to the
minimal solution of a certain fractional sublinear elliptic equation.
