Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion

We study the hydrodynamic limit for a model of symmetric exclusion processes with long jumps heavy-tailed and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators that are given by the regional fractional Laplacian with some additional reaction terms and various boundary conditions. This work solves some questions left open in \cite{BJGO2} about the same model.