Two models of the propagation of a disturbance in fractal media have been studied. The first model is based on the Poisson random walk and in a limiting case can be reduced to wave equation. The second model is a modification for a midpoint fractal lattice Feynman's path integral representation for the 1/2 spin. quantum relativistic propagator. For both of these models the problem of finding the probability of exit of a particle from the half-plane with Sierpinski carpets tesselation and midpoint fractal lattice, respectively, was considered.
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