Time-fractional kinetic equation for the non-Markovian kinetic processes

TL;DR

This paper develops a path integral framework for non-Markovian kinetic processes using time-fractional equations, enabling analysis of complex systems like ion channels and network dynamics.

Contribution

It introduces an analytical formulation of path integral representations for non-Markovian processes and generalizes solutions from Markovian to non-Markovian cases.

Findings

Path integral representation for non-Markovian processes derived.

Time-fractional kinetic equations formulated analytically.

Applicable to physical systems like ion channels and networks.

Abstract

In this study, we analytically formulated the path integral representation of the conditional probabilities for non-Markovian kinetic processes in terms of the free energy of the thermodynamic system. We carry out analytically the time-fractional kinetic equations for these processes. Thus, in a simple way, we generalize path integral solutions of the Markovian to the non-Markovian cases. We conclude that these pedagogical results can be applied to some physical problems such as the deformed ion channels, internet networks and non-equilibrium phase transition problems.