Fractional contact model in the continuum

TL;DR

This paper introduces a fractional evolution approach to the contact model in the continuum, incorporating memory effects that significantly alter the behavior of correlation functions compared to the standard model.

Contribution

It presents a non-Markov fractional evolution framework for the contact model, highlighting the impact of memory effects on correlation dynamics.

Findings

Correlation functions exhibit different time-dependent behavior due to fractional dynamics.

Memory effects significantly alter the evolution of the system.

The model provides new insights into non-Markovian statistical processes.

Abstract

We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a behavior of time-dependent correlation functions, essentially different from the one known for the standard contact model.