examples. T work made for analyzing the finite time stability of impulsive nonlinear delay damped system with caputo fractional derivative of orders and . S conditions which are derived from extended form of G inequality to analyze the stability in the finite range of time for such multi term fractional order impulsive control system. T potential of the proposed approach is demonstrated with the support of two numerical. Finite-Time Stability of Impulsive Fractional-Order Time Delay Systems with Damping Behavior. DNC. 2026;12(1):23-33. doi:10.5890/DNC.2023.03.003