  This paper derives physically meaningful boundary conditions for fractional
diffusion equations, using a mass balance approach. Numerical solutions are
presented, and theoretical properties are reviewed, including well-posedness
and steady state solutions. Absorbing and reflecting boundary conditions are
considered, and illustrated through several examples. Reflecting boundary
conditions involve fractional derivatives. The Caputo fractional derivative is
shown to be unsuitable for modeling fractional diffusion, since the resulting
boundary value problem is not positivity preserving.
