IMPULSIVE CONTROL IN FUZZY NEUTRAL SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper investigates the controllability of impulsive second-order neutral fuzzy functional differential systems with delay. Using the Banach fixed-point theorem and the framework of fuzzy numbers represented through their $\alpha$-level sets, we derive sufficient conditions for controllability and for the existence and uniqueness of fuzzy mild solutions. An explicit admissible control is constructed through the inverse of the $\alpha$-level controllability operator. The contraction condition incorporates the Lipschitz constants of the neutral and nonlinear terms, the impulse contribution, and a uniform bound for the inverse controllability operator. Two illustrative examples demonstrate how the assumptions and terminal-state controllability criterion can be verified. The proposed framework provides a unified analytical approach for impulsive neutral systems affected by uncertainty, delay, and abrupt state changes.