Behavior of fractional diffusion at the origin.
The present work discusses the fractional diffusion equation based on the Riemann-Liouville fractional time derivatives. It was shown that the normalization conservation constraint leads to the divergency of diffusive agent concentration at the origin. This divergency implies an external source of the diffusive agent at r-->0. Thus, the Riemann-Liouville fractional time derivative implies a loss of diffusive agent mass, which is compensated for by the source of this agent at the origin. In contrast, the absence of the normalization conservation constraint does not lead to any divergences in the limit r-->0 and at the same time provides the decay of normalization.
Ryabov
Ya E
YE
Department of Applied Physics, School of Applied Science, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel. Ryabov@vms.huji.ac.il