Langevin neutral impulsive fractional stochastic system along fractional Brownian motion-A controllability analysis

The purpose of this work is to investigate the controllability of Langevin-type stochastic neutral impulsive integro-differential equations governed by the Caputo fractional derivative and driven by fractional Brownian motion, which arise naturally in systems exhibiting memory, impulsive effects, and stochastic disturbances. Using resolvent operators and fixed-point techniques, necessary and sufficient controllability conditions are established for the associated linear system, while the controllability of the nonlinear system is demonstrated via the Banach contraction principle. The theoretical results confirm that appropriate control functions can steer the system to a desired state within a finite time interval. Finally, illustrative numerical examples are provided to demonstrate the applicability and effectiveness of the obtained results, highlighting their relevance to practical stochastic control problems.