  This manuscript explores a new class of non-autonomous second-order
stochastic inclusions of Clarke's subdifferential form with non-instantaneous
impulses (NIIs), unbounded delay and the Rosenblatt process in Hilbert spaces.
The existence of a solution is deduced by employing a fixed point strategy for
a set-valued map together with the evolution operator and stochastic analysis
approach. An example is analyzed for theoretical developments.
