الفهرس 
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Abstract
Representing real-life scenarios and converting them into mathematical models requires the use of nonlocal problems that incorporate both functional and differential equations. Assuring the credibility of these models requires integrating the concepts of Hyers-Ulam stability and continuous dependence. This integration is vital for evaluating how the models respond to slight disturbances, shedding light on their robustness and reliability. Hyers-Ulam stability, when applied to the problem specifically, evaluates the model’s robustness to disturbances, while Continuous dependence is applied to the unique solution of a problem to examine how the solutions are affected when its parameters are changed slightly.we study the uniqueness of the solution. Additionally, we study the Hyers-Ulam stability of the problem. Moreover, we investigate the continuous dependence of the unique solution on the initial data 𝑥, the functions 𝑔 and 𝑓, and parameters ρ and ϱ. Finally, we introduce some examples and special cases to illustrate our results.