Analysis on controllability of ψ-Hilfer fractional neutral stochastic differential system

This paper investigates the exact controllability of a [Formula: see text]-Hilfer fractional stochastic differential system. The main results are developed using tools from fractional calculus, infinitesimal generators, semigroup theory, stochastic analysis, and the Banach fixed point theorem. First, we derive the mild solution of the [Formula: see text]-Hilfer fractional stochastic system via the Laplace transform. We then establish the existence and uniqueness of this mild solution. Subsequently, the system is extended by introducing a control function, and its exact controllability is rigorously proved. Finally, an example is provided to illustrate and validate the theoretical findings.