In the article the general analysis identification of the problem for the law of the probability distribution of the observed random process (structural-parametric identification and comparative analysis of modern methods of identification of probability distributions showed, that at the present time to solve this problem is widespread method of normalized range (R/S analysis). Use this method when selecting a parametric model of the probability distribution best fits the experimental results, and minimal assumptions about the process under study and sufficient stability analysis of time series describing the investigated process. Information analysis method normalized range allowed us to propose a modified method for identification of the distribution law of random processes based on the normalized range (R/S analysis), for which the expressions for the elasticity and conditionality.

Keywords: diagnosis of technical systems, the method of normalized amplitude (RS analysis), method of Hirst, information analysis, the conditionality of the problem, the elasticity of the task

The article considers the problem of constructing a fractal model magnetoplasma electrodynamic accelerator. Modeling such a complex system is defined as the process of computing a generalized solution of the Fokker–Planck–Kolmogorov equation, describing real physical processes in hereditary (hereditarity) systems. The obtained Markov model, which determines the navigation system on multifractal sets of States along the trajectory of dispersal in a magnetoplasma electrodynamic accelerator, according to the research, is determined by the fractal dimension and the mathematical apparatus of generalized fractional derivatives of Riemann-Liouville. We have investigated the solutions of this equation, obtained after synthesis for fractional derivatives of Riemann–Liouville. The transition to fractional order derivative in time allows to take into account the temporal and spatial effects of system memory, processes in which processes are classified as "residual" memory, part of which is preserved, and the other part corresponds to irreversible losses.

Keywords: magnetoplasma electrodynamic accelerator (ED), hereditary (hereditarity) model of the system, the equation of the Fokker–Planck–Kolmogorov, fractional derivatives of Riemann–Liouville