TITLE:
Practical Mittag-Leffler Stability of Caputo Fractional Differential Equations with State-Dependent Delay and Perturbations
AUTHORS:
Fuhong Zhang, Xiaolan Liu
KEYWORDS:
State-Dependent Delays, Parameter Uncertainties, Lyapunov Functional, LMI
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.9,
September
16,
2026
ABSTRACT: In this paper, we investigate the locally practical Mittag-Leffler stability for a class of Caputo fractional-order differential equations subject to state-dependent delays and perturbations. By constructing an appropriate Lyapunov functional and employing key lemmas in fractional calculus, we derive a novel stability criterion under a weakened linear matrix inequality (LMI) condition. This criterion provides sufficient conditions for local practical Mittag-Leffler stability. The system state is bounded by the Mittag-Leffler function and the upper bound of perturbations, which can resist the influences of state-dependent delay and bounded perturbations. Finally, two numerical examples are provided to validate the correctness and effectiveness of the main theoretical results.