Boundary Conditions for Fractional Diffusion
Provides foundational boundary conditions for fractional diffusion models, relevant to researchers in applied mathematics and physics.
The paper derives physically meaningful boundary conditions for fractional diffusion equations using a mass balance approach, demonstrating that Caputo fractional derivatives are unsuitable due to lack of positivity preservation.
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.