Boundary value problems for fractional diffusion equations

Ralf Metzler, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

473 Scopus citations

Abstract

The fractional diffusion equation is solved for different boundary value problems, these being absorbing and reflecting boundaries in half-space and in a box. Thereby, the method of images and the Fourier-Laplace transformation technique are employed. The separation of variables is studied for a fractional diffusion equation with a potential term, describing a generalisation of an escape problem through a fluctuating bottleneck. The results lead to a further understanding of the fractional framework in the description of complex systems which exhibit anomalous diffusion.

Original languageEnglish
Pages (from-to)107-125
Number of pages19
JournalPhysica A: Statistical Mechanics and its Applications
Volume278
Issue number1
DOIs
StatePublished - 1 Apr 2000

Funding

FundersFunder number
Amos de Shalit
Alexander von Humboldt-Stiftung
Minerva Foundation

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