Directed transport of fractional Brownian motor driven by a temporal asymmetry force

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 algorithm, 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.