Kinetic properties of fractal media
  Kinetic processes in fractal stellar media are analysed in terms of the
approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving
a generalization of the nearest neighbour and random force distributions to
fractal media. Diffusion is investigated in the approximation of
scale-dependent conditional density based on an analysis of the solutions of
the corresponding Langevin equations. It is shown that kinetic parameters (time
scales, coefficients of dynamic friction, diffusion, etc.) for fractal stellar
media can differ significantly both qualitatively and quantitatively from the
corresponding parameters for a quasi-uniform random media with limited
fluctuations. The most important difference is that in the fractal case kinetic
parameters depend on spatial scale length and fractal dimension of the medium
studied. A generalized kinetic equation for stellar media (fundamental equation
of stellar dynamics) is derived in the Fokker-Planck approximation with the
allowance for the fractal properties of the spatial stellar density
distribution. Also derived are its limit forms that can be used to describe
small departures of fractal gravitating medium from equilibrium.
