Mean-square asymptotic stability of fractional-order nonlinear stochastic dynamic system

In this paper, the mean-square asymptotic stability problem is investigated for the fractional-order nonlinear stochastic dynamic system in Hilbert space. First, a set of sufficient stability conditions based on the Mittag–Leffler function is established to achieve the mean-square asymptotic stability of the system under the Lipschitz condition and linear growth condition, respectively. Next, the convergence analysis of the closed-loop system is finished by directly utilizing the properties of the integral solution and Mittag–Leffler function. Furthermore, in Euclidean space, the mean-square asymptotic stability problem is addressed for the fractional-order nonlinear stochastic dynamic system, in which sufficient stability conditions are given based on the eigenvalues of the matrix operator. Finally, two numerical examples are performed to verify the correctness of the proposed theoretical results.