Anomalous Diffusion with Periodical Initial Conditions on Interval with Reflecting Edges

Abstract

Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and etc. In this model a coordinate of a particle has stable distribution (not normal one). As a result a density of its distribution function satisfies an analog of diffusion equation in which second derivative by coordinate is replaced by partial derivative. In this paper the anomalous diffusion with periodic initial conditions on an interval with reflecting edges is considered. Such problem is important for example in technical mechanics for an analysis of fuel mixing in straight flow engine too. As A.A. Borovkov suggested special probability methods are developed to analyze such a diffusion.