Stochastic Simulation of Fractional Dynamics

Abstract

Theoretical formalisms based on fractional differential equations are increasingly being used to model complex kinetic processes, as they can accurately capture memory effects and temporal heterogeneity. This study proposes a stochastic simulation methodology for processes governed by such equations. The numerical implementation uses a discrete-time Monte Carlo algorithm to model the evolution of an irreversible unimolecular reaction by integrating Mittag-Leffler statistics directly into the dynamics of microscopic events. The study concludes that the proposed method is robust and consistently recovers the classical limit, thereby establishing a rigorous link between fractional chemical kinetics and computational simulation. Consequently, this approach constitutes a powerful predictive framework for chemical systems in complex media.