examples., This work made for analyzing the finite-time stability of impulsive nonlinear delay damped system with caputo fractional derivative of orders and . Sufficient conditions which are derived from extended form of Gronwall's inequality to analyze the stability in the finite range of time for such multi-term fractional-order impulsive control system. The potential of the proposed approach is demonstrated with the support of two numerical. 2026. “Finite-Time Stability of Impulsive Fractional-Order Time Delay Systems With Damping Behavior”. Discontinuity, Nonlinearity, and Complexity 12 (1): 23-33. https://doi.org/10.5890/DNC.2023.03.003.