Work

Stability analysis of stochastic systems with fractional dynamics

Year: 2026

Type: article

Abstract: This paper investigates the stability properties of stochastic functional differential equations driven by fractional Brownian motion (FBM), a natural extension of classical Brownian motion that incorporates memory effects through the Hurst parameter. By constructing appropriate Lyapunov functionals, we derive sufficient conditions for global exponential mean square stability and asymptotic stochastic stability. The analysis is applied to a delayed stochastic fractional Black–Scholes model, where explicit criteria for both stability types are established. Numerical simulations are presented to validate the theoretical results and illustrate the influence of the Hurst index on the stability behavior of the system.

Source: Journal of low frequency noise, vibration and active control

DOI: 10.1177/14613484251382645

Authors: Nabil A. Ibrahim, Islam M. Elbaz, Hesham G. Abdelwahed, Ali A. El-Rahman, Mahmoud A. E. Abdelrahman, Mohamed A. Sohaly