  We analyse the hydrodynamical behavior of the long jumps symmetric exclusion
process in the presence of a slow barrier. The jump rates are given by a
symmetric transition probability $p(\cdot)$ with infinite variance. When jumps
occur from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$ the rates are slowed down by a
factor $\alpha n^{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$). We obtain
several partial differential equations given in terms of the regional
fractional Laplacian on $\mathbb R^*$ and with different boundary conditions.
Surprisingly, in opposition to the diffusive regime, we get different regimes
depending on whether $\alpha=1$ (all bonds with the same rate) or $\alpha\neq
1$.
