  This paper considers a class of nonlocal fractional neutral stochastic
integrodifferential inclusions of order $1<\alpha<2$ with impulses in a Hilbert
space. We study the existence of the mild solution for the cases when the
multi-valued map has convex and non-convex values. The results are obtained by
combining fixed-point theorems with the fractional order cosine family,
semigroup theory, and stochastic techniques. A new set of sufficient conditions
is developed to demonstrate the approximate controllability of the system.
Finally, an example is given to illustrate the obtained results.
