Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion

We study the hydrodynamic limit for symmetric exclusion processes with heavy-tailed long jumps 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. Here we answer to all the questions left open in Bernardin et al. (2021) and we prove a conjecture stated in that same article & COPY; 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).