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. (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