2025 , Volume 30, № 1, p.41-50

We have established that in subdiffusion models with delays, the methods of direct stochastic random walk have advantages over difference methods for numerical implementation of equivalent models in the form of integral equations or in the form of equations with fractional time derivatives. It follows from the axioms behind the random walk models. The temporal and algorithmic advantages of the stochastic method are established. It is revealed that it allows tracking the individual behavior of groups of tagged particles and comparing this behavior with the collective behavior of an ensemble of particles. For the stochastic model, a theoretical justification and experimental confirmation are given that the distribution of the residuals of the particle delay time depends on the time of their random walk. A method for determining the diffusion parameters is proposed for studying processes that are observed after the initial moment of time.