Controllability of non-instantaneous impulsive large-scale neutral fractional stochastic systems with Poisson jumps

Non-instantaneous impulsive dierential equations can be applied in various areas of inclusive health and social determinants of health, contributing to the understanding and management of complex health-related phenomena. This manuscript presents a study on controllability of non-instantaneous impulsive large-scale neutral fractional stochastic systems with Poisson jumps (NILNFSP) in finite dimensional space. Firstly, we present the solution representation of the linear and nonlinear systems using Laplace transform. Based on the solution of considered linear system, Grammian matrices are constructed for the m-non-instantaneous impulsive intervals. Thereafter, sufficient conditions for controllability result of the nonlinear systems are derived by employing Mönch fixed point theorem, suitable hypothesis on nonlinear terms and stochastic inequalities. Finally, an example is provided to check all the necessary assumptions of the derived theoretical result.