FTS for a class of proportional fractional Itô–Doob stochastic time delayed systems

Abstract This paper addresses the finite time stability (FTS) of proportional fractional Itô–Doob stochastic systems with time delays. It begins by defining the key concepts and mathematical formulations necessary for understanding these systems. The main contributions include the derivation of sufficient FTS conditions using some mathematical inequalities, which integrates proportional fractional calculus, stochastic analysis, and time‐delay compensation. The paper also presents an example to verify the theoretical bounds. The findings provide a comprehensive perspective on stochastic fractional control, highlighting the importance of addressing time delays and stochasticity in fractional‐order systems.