  We consider a family of fractional porous media equations, recently studied
by Caffarelli and V\'azquez. We show the construction of a weak solution as
Wasserstein gradient flow of a square fractional Sobolev norm. Energy
dissipation inequality, regularizing effect and decay estimates for the $L^p$
norms are established. Moreover, we show that a classical porous medium
equation can be obtained as a limit case.
