  In this paper we complement the program concerning the application of
symmetrization methods to nonlocal PDEs by providing new estimates, in the
sense of mass concentration comparison, for solutions to linear fractional
elliptic and parabolic PDEs with Neumann boundary conditions. These results are
achieved by employing suitable symmetrization arguments to the Stinga-Torrea
local extension problems, corresponding to the fractional boundary value
problems considered. Sharp estimates are obtained first for elliptic equations
and a certain number of consequences in terms of regularity estimates is then
established. Finally, a parabolic symmetrization result is covered as an
application of the elliptic concentration estimates in the implicit time
discretization scheme.
