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 examples., “Finite-Time Stability of Impulsive Fractional-Order Time Delay Systems with Damping Behavior”, DNC, vol. 12, no. 1, pp. 23–33, Aug. 2026, doi: 10.5890/DNC.2023.03.003.