Approximate controllability results for Hilfer fractional neutral stochastic differential equations with finite delay and non‐dense domain

Abstract In this work, we analyze a class of Hilfer fractional neutral stochastic differential equations with finite delay in a non‐dense domain. We establish existence and uniqueness results using analytical tools from fractional calculus, semigroup theory, stochastic analysis, and fixed‐point techniques. A set of assumptions is introduced to guarantee the existence and uniqueness of solutions. Furthermore, a set of hypotheses is provided to examine the approximate controllability of the system. An illustrative example is provided to highlight the theoretical developments.