We investigate the fractional diffusion limit of a Linear Boltzmann equation
with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary
conditions. We derive a new confined version of the fractional Laplacian and
show uniqueness of weak solutions to the associated non-local diffusion
equation. This paper extends previous results of L. Cesbron, A. Mellet and M.
Puel [5] on the same kinetic model with diffusive boundary conditions