Boundary conditions for fractional diffusion

• 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 positivitypreserving.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Fractional calculus

Boundary value problem

Numerical solution

Well-posed

partial-differential-equations

advection-dispersion equation

continuous-time finance

anomalous diffusion

numerical-solution

vector

calculus

order

approximations

transport

dynamics

Mathematics

Well-posed

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)