Barkai E, Metzler R, Klafter J
Department of Chemistry and Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):132-8. doi: 10.1103/physreve.61.132.
We generalize the continuous time random walk (CTRW) to include the effect of space dependent jump probabilities. When the mean waiting time diverges we derive a fractional Fokker-Planck equation (FFPE). This equation describes anomalous diffusion in an external force field and close to thermal equilibrium. We discuss the domain of validity of the fractional kinetic equation. For the force free case we compare between the CTRW solution and that of the FFPE.
我们将连续时间随机游走（CTRW）进行推广，以纳入空间依赖跳跃概率的影响。当平均等待时间发散时，我们推导出一个分数阶福克 - 普朗克方程（FFPE）。该方程描述了外力场中且接近热平衡时的反常扩散。我们讨论了分数阶动力学方程的有效性范围。对于无外力情况，我们比较了CTRW解和FFPE解。
