  We investigate the fractional diffusion approximation of a kinetic equation
in the upper-half plane with diffusive reflection conditions at the boundary.
In an appropriate singular limit corresponding to small Knudsen number and long
time asymptotic, we derive a fractional diffusion equation with a nonlocal
Neumann boundary condition for the density of particles. Interestingly, this
asymptotic equation is different from the one derived by L. Cesbron in [7] in
the case of specular reflection conditions at the boundary and does not seem to
have receive a lot of attention previously.
