Boundary value problems for fractional diffusion equations

Ralf Metzler and Joseph Klafter

Physica A: Statistical Mechanics and its Applications, 2000, vol. 278, issue 1, 107-125

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.

Keywords: Fractional diffusion equation; Boundary value problems; Mittag–Leffler relaxation; Anomalous diffusion; Anomalous relaxation (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (32)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:278:y:2000:i:1:p:107-125

DOI: 10.1016/S0378-4371(99)00503-8

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