This research delves into the investigation of a nonlocal problem characterized by a delay functional differential equation with parameter under the influence of an internal integro-differential condition. Under appropriate assumptions in place, our central objective is to establish the existence and uniqueness of solutions, a task facilitated by the application of the Schauder fixed point theorem.
Additionally, we employ the Hyers-Ulam stability concept to thoroughly analyze the stability properties of the problem when subjected to slight perturbations in order to ensure the credibility of the problem.
Furthermore, we conduct a specific investigation into the continuous dependence of the unique solution on various factors, providing insights into how changes in these factors affect the behavior of the solution.
The combination of the Hyers-Ulam stability concept and the continuous dependence provides a robust framework for conducting a thorough stability analysis of the problem.
The study not only contributes to theoretical understanding but also provides practical insights across the analysis of specific cases and instances.