Reprint of: Boundary conditions for fractional diffusion
Journal article, 2018

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.

Boundary value problem

Fractional calculus

Well-posed

Numerical solution

Author

Boris Baeumer

University of Otago

Mihaly Kovacs

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mark M. Meerschaert

Michigan State University

Harish Sankaranarayanan

Michigan State University

Journal of Computational and Applied Mathematics

0377-0427 (ISSN)

Vol. 339 414-430

Subject Categories

Applied Mechanics

Computational Mathematics

Mathematical Analysis

DOI

10.1016/j.cam.2018.03.007

More information

Latest update

6/24/2019