Fractional Diffusion based on RiemannLiouville Fractional Derivatives
Abstract
A fractional diffusion equation based on RiemannLiouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of $H$functions. It differs from the known solution of fractional diffusion equations based on fractional integrals. The solution of fractional diffusion based on a RiemannLiouville fractional time derivative does not admit a probabilistic interpretation in contrast with fractional diffusion based on fractional integrals. While the fractional initial value problem is well defined and the solution finite at all times its values for $t\to 0$ are divergent.
 Publication:

arXiv eprints
 Pub Date:
 June 2000
 arXiv:
 arXiv:condmat/0006427
 Bibcode:
 2000cond.mat..6427H
 Keywords:

 Statistical Mechanics;
 Disordered Systems and Neural Networks
 EPrint:
 11 pages, Latex