This study establishes novel sufficient conditions to guarantee the well-posedness and Hyers-Ulam stability of solutions for a class of nonlinear \(\psi \) -fractional integro-differential equations subject to functional boundary constraints. By employing fixed-point theorems (Banach’s contraction principle, and Leray-Schauder’s theorem), multivariate Mittag-Leffler functions, and Babenko’s approach, we derive rigorous analytical criteria for the solvability and stability of the proposed equation. Furthermore, we investigate Hyers–Ulam stability to quantify the robustness of solutions under perturbations. Two examples are presented to validate the theoretical findings. This study contributes to the broader understanding of \(\psi \) -fractional integro-differential systems by introducing a flexible framework for analyzing nonlinear dynamics under functional constraints.
