This paper focuses to establish the sufficient conditions for the existence of the integral form mild solution and the approximate controllability for a class of the nonlinear fractional neutral-type integro-differential delayed stochastic system with the instantaneous impulsive effects in a separable Hilbert space by considering the \(\Psi \) -Caputo fractional derivative. A key advantage of employing the \(\Psi \) -Caputo fractional derivative is its inherent flexibility in choosing a suitable kernel function \(\Psi \) , which enhances its compatibility with conventional analytical techniques. Firstly, we derive the existence of the mild solution for the \(\Psi \) -Caputo fractional neutral-type delayed integro-differential stochastic system. For this purpose, the proposed stochastic control problem is transferred into an equivalent fixed-point problem using the \(\Psi \) -Riemann-Liouville fractional integral operator. Then, the Schauder fixed point theorem is applied. By employing tools from fractional calculus, Laplace transforms, stochastic analysis and fixed point theorem, the set of sufficient conditions is established. The approximate controllability result is established under the consideration that the corresponding linear system is approximately controllable. To illustrate the abstract results, we provide an example at the end of the paper.
