Controllability of second order neutral impulsive fuzzy functional differential equations with Non-Local conditions

In this paper, the controllability of fuzzy solutions for a second-order nonlocal impulsive neutral functional differential equation with both nonlocal and impulsive conditions in terms of fuzzy are considered. The sufficient condition of controllability is developed using the Banach fixed point theorem and a fuzzy number whose values are normal, convex, upper semi-continuous, and compactly supported fuzzy sets with the Hausdorff distance between α -cuts at its maximum. The α -cut approaches allow to translate a system of fuzzy differential equations into a system of ordinary differential equations to the endpoints of the states. An example of the application is given at the end to demonstrate the results. These kinds of systems come in use for designing landing systems for planes and spacecraft, as well as car suspension systems.