Fractional Brownian motor and its directed transport

Abstract

Adopting power function as a damping kernel function of generalized Langevin equation, flash ratchet potential as a potential field, the model of fractional Brownian motor is derived in the case of overdamped condition. With the memory effect of fractional derivatives, the motion characteristics of the particle in overdamped fractional Brownian motor are discussed. Inverse transport which is not seen in conventional Brownian motor, is found in an overdamped fractional Brownian motor. The influences of fractional order and noise density on transport speed are discussed separately. For a fixed fractional order, stochastic resonance appears in transport speed as noise density varies. For a fixed noise density, transport speed will oscillate as the fractional order varies, that is, multipeak generalized stochastic resonance takes place.