近年来，随着实验技术的发展，人们发现了大量表现出反常输运行为的系统。Lévy飞行就是其中重要的一类。本文主要利用Langevin方程和分数Fokker-Planck方程研究Lévy飞行相关的问题。首先我们考虑到了Langevin方程中的惯性项，讨论了外势场中的惯性Lévy飞行，并分析了有限阻尼系数对粒子动力学的影响。其次，研究了在Langevin方程中引入非线性阻尼作用后的Lévy飞行。发现引入非线性阻尼项后，粒子速度及坐标的二次矩是有限的。最后考虑到噪声的关联，研究了色Lévy噪声驱动下的Lévy飞行在外势场中的动力学行为，并分析了关联Lévy棘轮模型产生定向流的机制。

In recent years, with the development of experimental technique, numbers of systems that act anomalous transport have been discovered. Among these, Lévy flight is one of the most important one. In this paper, both Langevin equation and FFPE are used to study the questions related to the Lévy flight. Firstly, we include the inertial term in the Langevin equation and discussed the inertial Lévy flight in the external potentials. Then the Lévy flight with nonlinear friction is studied. Finally, the correlated Lévy flight is investigated and we analyze the mechanism of the correlated Lévy ratchet.