In this paper we answer positively a question raised by Metzler and Klafter [Phys. Rep. 339, 1 (2000)]: can one see a competition between subdiffusion and Lévy flights in the framework of the fractional Fokker-Planck dynamics? Our method of Monte Carlo simulations demonstrates the competition on the level of realizations as well as on the level of probability density functions of the anomalous diffusion process. The simulation algorithm is based on a stochastic representation of the above dynamics.
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