2000/06/27 by R. Hilfer
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.dis-nn
published as J.Phys.Chem B, vol. 104, page 3914, (2000) · 11 pages, Latex
arxiv created 2000/06/27 · arxiv updated 2009/11/30
A fractional diffusion equation based on Riemann-Liouville 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 Riemann-Liouville 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→ 0 are divergent.