A Novel Fractional-Order Model for Alcohol Consumption Dynamics: Evaluating Social and Economic Interventions

In this paper, we propose a new fractional-order mathematical model of alcohol drinking behavior involving the conformable fractional derivative $\mathcal{CFD}$ and eight interconnected compartments, incorporating the socio-economic distinction between private and public addiction treatment centers. The model explicitly accounts for road accidents and alcohol-induced violence as separate classes, emphasizing the societal impact of heavy drinking. We establish the existence and uniqueness of solutions and analyze the Ulam-Hyers (U-H) stability of the model using fixed-point theory, ensuring the robustness of the theoretical framework. Numerical simulations further validate the theoretical results under varying fractional orders of $\mathcal{CFD}$, demonstrating that higher memory effects in fractional dynamics lead to slower addiction recovery and prolonged intervention impact. Additionally, model validation using real-time data reinforces its applicability to real-world scenarios, demonstrating the model‘s potential for guiding policy decisions and treatment strategies.