This paper investigates the finite-time stability (FTS) of a class of fractional-order fuzzy inertial neural networks (FOFINNs) with time-varying delays. The existing finite-time inequalities for fractional-order systems pose significant theoretical and practical limitations, as they can yield unbounded control inputs when the system state approaches zero. To address this issue, this work introduces a novel finite-time inequality. By incorporating a positive constant into the inequality structure, the proposed method effectively bounds the control signal, ensuring its practical realizability. Utilizing this inequality within a Lyapunov framework alongside an order reduction method (ORM), a composite feedback controller is designed to achieve FTS. Sufficient stability conditions are derived, and an explicit, computable upper bound for the settling time is established. Numerical simulations validate the theoretical results and demonstrate the method's superiority over existing approaches.

This paper explored the finite-time stability (FTS) of fractional-order fuzzy inertial neural network with mixed delays. First, the dimension of the model was reduced by the order reduction method. Second, by leveraging the fractional-order finite-time stability theorem, fractional calculus and inequality methods, we established some sufficient conditions to guarantee the FTS of the model under feasible delay-dependent feedback controller and delay-dependent adaptive controller, respectively. Additionally, we derived the settling times (STs) for each control strategy. Finally, we provided two examples to substantiate our findings.