Boundary value problems for fractional diffusion equations

The fractional diffusion equation is solved for different boundary value pr oblems, these being absorbing and reflecting boundaries in half-space and i n a box. Thereby, the method of images and the Fouker-Laplace transformatio n technique are employed. The separation of variables is studied for a frac tional diffusion equation with a potential term, describing a generalisatio n of an escape problem through a fluctuating bottleneck. The results lead t o a further understanding of the fractional framework in the description of complex systems which exhibit anomalous diffusion. (C) 2000 Elsevier Scien ce B.V. All rights reserved.