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. Discontinuity, Nonlinearity, and Complexity, v. 12, n. 1, p. 23–33, 17 Aug.2026.