AUTOMODELITY AS A CHARACTERISTIC PROPERTY OF NONLOCAL ANOMALOUS DIFFUSION
A brief presentation of the relationship between a non-Gaussian family of stable laws and the self-similarity of the nonlocal processes described by them. The characteristic property of self-similarity makes it possible to arrange the ballistic, Brownian, and Levy-models of motion in a logically connected chain with characteristic exponents a = 1,2 and 0 < a < 2, which determine the degrees of differential operators describing these movements. The family of models generated by fractional values of a is characterized by a specific property of nonlocality, which is reflected in the physical interpretation in terms of fractality, if we are talking about the spatial derivative, and heredity, in the case of time-differentiation.