Approximate controllability of higher-order Sobolev-type stochastic AB-fractional differential inclusions with impulses and Clarke sub-differentials

In this paper, we investigated the existence of mild solutions and the approximate controllability of a novel class of Sobolev-type stochastic impulsive differential inclusions driven by a higher-order Atangana–Baleanu fractional derivative in the Caputo sense. The system is formulated in an infinite-dimensional framework and incorporates Brownian motion processes, impulsive effects, and non-smooth multi-valued nonlinearities described via Clarke's generalized sub-differential. By employing methods from fractional evolution theory, stochastic analysis, and multi-valued fixed-point theory, we established sufficient conditions for solvability and approximate controllability. The results extended classical controllability frameworks to systems exhibiting memory, randomness, and impulsive dynamics. An illustrative example is provided to demonstrate the applicability of the theoretical findings.