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.