Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902122 | Journal of Computational and Applied Mathematics | 2018 | 30 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Boris Baeumer, Mihály Kovács, Mark M. Meerschaert, Harish Sankaranarayanan,