This paper investigates a new class of \(\Psi\) -fractional iterative differential equations subject to a state-dependent nonlocal condition, introduced by Hernández and O’Regan [1]. By reformulating the problem into an equivalent \({\rm{\Psi }}\) -fractional integral equation, we establish sufficient conditions for the existence and uniqueness of solutions using the fixed-point techniques, notably Schauder’s and Banach’s fixed-point theorems. We also demonstrate the continuous dependence on data of the solution of the problem setting. Furthermore, we explore both Ulam–Hyers and generalized Ulam–Hyers stability, providing explicit criteria. Two illustrative examples are presented to validate the theoretical findings.
