  We formulate a numerical method to solve the porous medium type equation with
fractional diffusion \[\frac{\partial u}{\partial t}+(-\Delta)^{1/2} (u^m)=0.\]
The problem is posed in $x\in \mathbb{R}^N$, $m\geq 1$ and with nonnegative
initial data. The fractional Laplacian is implemented via the so-called
Caffarelli-Silvestre extension. We prove existence and uniqueness of the
solution of this method and also the convergence to the theoretical solution of
the equation. We run numerical experiments on typical initial data.
