Anomalous transports in a time-delayed system subjected to anomalous diffusion

We investigate anomalous transports of an inertial Brownian particle in a time-delayed periodic potential subjected to an external time-periodic force, a constant bias force, and the Lévy noise. By means of numerical calculations, effect of the time delay and the Lévy noise on its mean velocity are discussed. The results indicate that: (i) The time delay can induce both multiple current reversals (CRs) and absolute negative mobility (ANM) phenomena in the system; (ii) The CRs and ANM phenomena only take place in the region of superdiffusion, while disappear in the regions of normal diffusion; (iii) The time delay can cause state transition of the system from anomalous →normal→anomalous→normal→anomalous →normal transport in the case of superdiffusion.