Keywords: 
• 定向输运 /
• 布朗马达 /
• 分数阶郎之万方程 /
• 广义随机共振

Abstract: The directed transport of a Brownian particle in a spatially periodic symmetric field under a temporal asymmetric force is studied. Based on the Caputo’s fractional derivatives theory, we establish a differential aquation for an over-damped fractional Brownian motor as the system’s mathematic model, where the external force is zero-mean and the fractional order is used to describe the inhomogeneity of the real environment. Using the fractional differential algo-rithm, we analyze the relationships between transport velocity and model parameters. It is worth mentioning that the impact of fractional order is discussed in detail. According to the research we find that a temporal asymmetric force can induce a net current without the application of a ratchet potential, even a noise. We also find that the velocity of the current increases monotonically with the increase in fractional order. Moreover with certain fractional orders, a generalized resonance phenomenon is revealed since the velocity of the current varies non-monotonically with the system parameters, such as the height of the potential barrier and the noise strength etc. Research shows that the fractional system is a generalization of the traditional dynamic systems, which could probably give a more reasonable explanation of the directed transport as a consequence.