This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutralâtype fractional stochastic integrodifferential inclusions with infinite delay and nonâinstantaneous impulse in a separable Hilbert space using the AtanganaâBaleanu Caputo fractional derivative. We investigate the existence of a mild solution for the AtanganaâBaleanu Caputo fractional neutralâtype delay integrodifferential stochastic system while taking into account the nonâinstantaneous impulses. For this purpose, the AtanganaâBaleanu Caputo fractional neutralâtype impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the BohnenblustâKarlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper.