Finite time stability for a class of Hadamard fractional Itô–Doob stochastic time‐delayed systems

Abstract This paper addresses finite time stability for a class of Hadamard fractional Itô–Doob stochastic time‐delayed systems. A novel stability result is derived based on Gronwall‐type inequalities, thereby generalizing the classical integer order case to the fractional domain. In addition, our analysis uniquely integrates stochastic perturbations and time delays, providing a comprehensive framework for systems with both memory and randomness. An illustrative example of a three‐dimensional stochastic system with time delays and fractional dynamics demonstrates the effectiveness of the proposed approach.