This study develops a novel nonlinear fractional model of alcohol consumption using the Atangana–Baleanu Caputo (ABC) fractional derivative to capture memory-dependent dynamics. The model is formulated using advanced analytical techniques and implemented via the finite difference method, with key theorems established to ensure the existence, uniqueness, and stability of solutions. The basic reproduction number R_0 is derived, and a detailed sensitivity analysis is performed to assess the influence of model parameters on alcohol-use dynamics. The results show that when R_0<1, the alcohol-free equilibrium is both locally and globally asymptotically stable. Numerical simulations support the theoretical analysis, demonstrating strong convergence and accuracy. Importantly, the findings indicate that increasing treatment rates significantly reduces interactions between heavy and non-heavy drinkers, offering valuable insights for designing effective intervention strategies.
