Additive symmetric Levy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such Levy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the Levy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static Levy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive Levy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.
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