  We formulate a numerical method to solve the porous medium type equation with
fractional diffusion \[ \frac{\partial u}{\partial t}+(-\Delta)^{\sigma/2}
(u^m)=0 \] posed for $x\in \mathbb{R}^N$, $t>0$, with $m\geq 1$, $\sigma \in
(0,2)$, and nonnegative initial data $u(x,0)$. We prove existence and
uniqueness of the solution of the numerical method and also the convergence to
the theoretical solution of the equation with an order depending on $\sigma$.
We also propose a two points approximation to a $\sigma$-derivative with order
$O(h^{2-\sigma})$.
