中文摘要：

讨论了分数阶Frenkel—Kontorova模型的物理意义，并应用该模型刻画了耦合粒子链在记忆性介质中的输运现象，研究了各参数对粒子链运动状态的影响．数值仿真结果表明：系统的记忆性对粒子链的运动有显著影响，尤其出现了在非记忆性情况下所不具有的反向流．同时发现粒子链的平均流速会随耦合强度、分数阶的阶数变化而产生广义共振；此外，平均流速还会随噪声强度的变化出现广义随机共振现象．

英文摘要：

In this paper, we first discuss the physical meaning of the fractional Frenkel-Kontorova model and depict the transport phenomenon of elastically coupled particles in a memorable medium, then give the effects of various parameters on the motion of coupled particles. According to the numerical value, the memory effect of system has a significant influence on the motion of coupled particles, in addition, the current reversal which does not exist in a non-memorable system appears, this is an abnormal phenomenon. What is more in this research we find that there appears the generalized resonance in the system mean velocity as the spring constant and the fractional order are varied, and the generalized stochastic resonance will appear with noise intensity changing.