Effect of anomalous diffusion on directed motion in a multiplicative noise driven flashing ratchet system

In this paper we have studied the directed motion of a Brownian particle in a multiplicative noise driven flashing ratchet system. Our investigation shows the current (j) is either maximum or minimum in the super-diffusion (SPD) region depending on the asymmetric character of the ratchet potential. But the optimum behavior disappears for the symmetric ratchet potential and there is a current inversion around the normal diffusion (ND). With increase of half cycle period(t(p)/2) (which controls the on-off operation mechanism of the potential), j passes through a maximum and the peak height is the highest for the SPD. Also at low asymmetry in the system, the mobility is more dominating for the normal and the super-diffusion cases than the sub-diffusion. For large asymmetry in the ratchet potential, the diffusion control positive current is larger for the ND compared to the other cases. Finally, we observe that there is a maximum in the variation of current as a function of noise correlation time for SPD. But it disappears for the other cases.