We prove the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many reservoirs with density $$\alpha $$ at the left of the system and $$\beta $$ at the right of the system. The strength of the reservoirs is ruled by $$\kappa N^{-\theta }>0$$ . Here N is the size of the system, $$\kappa >0$$ and $$\theta \in {{\mathbb {R}}}$$ . Our results are valid for $$\theta \le 0$$ . For $$\theta =0$$ , we obtain a collection of fractional reaction–diffusion equations indexed by the parameter $$\kappa $$ and with Dirichlet boundary conditions. Their solutions also depend on $$\kappa $$ . For $$\theta <0$$ , the hydrodynamic equation corresponds to a reaction equation with Dirichlet boundary conditions. The case $$\theta > 0$$ is still open. For that reason we also analyze the convergence of the unique weak solution of the equation in the case $$\theta =0$$ when we send the parameter $$\kappa $$ to zero. Indeed, we conjecture that the limiting profile when $$\kappa \rightarrow 0$$ is the one that we should obtain when taking small values of $$\theta >0$$ .