  In this paper, the interrelations of some dynamical properties of the
non-autonomous dynamical system (X, f1;infinity) and its induced non-autonomous
dynamical system (K(X), f1;infinity) are studied, where K(X) is the hyperspace
of all non-empty compact subsets of X, endowed with Vietoris topology. Various
stronger forms of sensitivity and transitivity are considered. Some examples of
non-autonomous systems are provided to support the results. A relation between
shadowing property of the non- autonomous system (X, f1;infinity) and its
induced system (K(X), f1;infinity) is studied.
