Stability and controllability for Volterra integro-dynamical matrix Sylvester impulsive system on time scales

In this paper, we study Ulam's-Hyer stability and exact controllability results for Volterra integro-dynamic matrix Sylvester impulsive evolution system on time scales. By using the vectorization operator, we convert the Volterra integro-dynamic matrix Sylvester impulsive system on time scale to an equivalent Volterra integro-dynamic impulsive Kronecker product system on time scale. It has two sections: one on the stability of Ulam's-Hyer types and the other on the exact controllability results. We used the evolution operator theory, Banach fixed point theorem and nonlinear functional analysis to establish these results. Finally, we've given some numerical and theoretical examples of the way those advanced analytical consequences may be applied.