  Two models of anomalous diffusion of cosmic ray in the leaky-box
approximation are compared: one of them is based on the decoupled time-space
L\'evy flights and the other on fractional walks with a finite free motion
velocity. Distributions of first passage time and paths are computed and
evolution of diffusion packets to equilibrium state is shown. Calculations
demonstrate essential difference between the two models: the coupled scheme
gives more realistic results.
