Work

Asymptotic behavior of solutions for stochastic fractional differential equations involving bounded delay

Year: 2026

Type: article

Abstract: In this paper, we investigate the asymptotic mean-square behavior of solutions for a class of stochastic fractional delay differential equations (SFDDEs) when the fractional derivative is in the Caputo sense. To this end, we first establish a variation of constants formula for the considered system. Subsequently, by employing the Jordan normal form of matrices together with a Djrbashian-type summation formula, we obtain precise estimates for the matrix-form Mittag-Leffler function. We then construct a suitable weighted norm and utilize its favorable properties to establish the desired asymptotic results. Crucially, this tailored weighted-norm approach isolates the asymptotic tail behavior of the solution, allowing us to completely remove the restrictive 2 η scaling condition typically imposed on delay Lipschitz constants by standard fractional Halanay inequalities, where η is fractional order. These findings contribute to the qualitative analysis of stochastic fractional differential systems with delays, providing sharper stability criteria and new insights into their long-term stability in the mean-square sense. Finally, we present some numerical simulations to support the theoretical results.

Source: Chaos Solitons & Fractals

DOI: 10.1016/j.chaos.2026.118996

Authors: Phan Thi Huong, Nguyen Nhu Thang

Institutions: Le Quy Don Technical University, Hanoi National University of Education

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,970

Funder: National Foundation for Science and Technology Development