Anomalous diffusion and fractional stable distributions

A new set of distributions, called fractional stable distributions, is described. A subset of this set is represented by stable laws, while its particular case is the Gaussian distribution. These distributions arise as solutions to fractional-order partial differential equations that represent a generalization of the ordinary diffusion equation to the case of anomalous diffusion. The properties of multidimensional fractional stable densities are described, their expressions in terms of special functions are presented, and physical problems that lead to these densities are discussed.