Abstract
We discuss two models for the description of anomalous diffusion, these being the continuous time random walk scheme, and fractional diffusion equations. We show their interrelations, and combine both approaches for the description of anomalous transport in constant external velocity and force fields. For an arbitrary external force F(x), we introduce a fractional Fokker-Planck equation, which generalises the two Einstein relations.
| Original language | English |
|---|---|
| Pages (from-to) | 343-350 |
| Number of pages | 8 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 266 |
| Issue number | 1-4 |
| DOIs | |
| State | Published - 15 Apr 1999 |
| Externally published | Yes |
| Event | Proceedings of the 1998 International Conference on Percolation and Disordered Systems: Theory and Applications - Giessen, Ger Duration: 14 Jul 1998 → 17 Jul 1998 |
Bibliographical note
Funding Information:RM is Feodor–Lynen fellow of the Alexander von Humboldt Stiftung, Bonn am Rhein, Germany. Financial support from the German Israeli Foundation (GIF) is acknowledged. We thank Igor Sokolov and Theo F. Nonnenmacher for helpful discussions. RM thanks Israela Becker for fruitful comments.