Stability analysis of stochastic systems with fractional dynamics

Journal of low frequency noise, vibration and active control 2026 Open access

Read full text
Authors: Nabil A. Ibrahim, Islam M. Elbaz, H. G. Abdelwahed, A.A. El-Rahman, Mahmoud A. E. Abdelrahman, Mohamed A. Sohaly
DOI: 10.1177/14613484251382645
Cited by: 0
References: 23

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.

Fields of Study & Subjects

Nonlinear Differential Equations Analysis Stability and Control of Uncertain Systems Stochastic processes and financial applications

Publication details

Journal / source
Journal of low frequency noise, vibration and active control
Volume
45
Issue
2
Pages
709–722
Publication date
13 January 2026
Language
EN