Abe Sumiyoshi
Department of Physical Engineering, Mie University, Mie 514-8507, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022142. doi: 10.1103/PhysRevE.88.022142. Epub 2013 Aug 27.
A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatiotemporal fractionality, and a variational solution is obtained with the help of the Lévy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.
基于辅助场形式主义，为分数动力学发展了一种变分原理。将其应用于具有时空分数阶性的福克 - 普朗克方程，并借助列维假设获得了变分解。展示了变分解如何通过长等待时间和长跳跃之间的竞争效应实现从亚扩散到超扩散的整个范围。在周期性漂移的情况下，还分析了概率分布中心的运动。
