Exponential Stability in the p-th Moment for Caputo Fractional Stochastic Delay Differential Systems

This paper investigates the dynamic behavior of Caputo-type fractional stochastic delay differential equations. We construct an Itô-Caputo differential formula associated with the Mittag-Leffler type matrix polynomial function. Utilizing this formula along with tools such as Hölder’s inequality, the Burkholder-Davis-Gundy (BDG) inequality, and Gronwall’s inequality, the p-th moment estimation bounds for the system’s solution are rigorously derived. Furthermore, by constructing stochastic differential operators and imposing several assumptions, a criterion for the p-th moment exponential stability of the system’s solution is established. Finally, numerical examples are provided to verify the effectiveness of the proposed theoretical results.