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

A study of nonlocal fractional neutral stochastic integrodifferential inclusions of order $1<\alpha<2$ with impulses