Mathematical analysis and numerical simulation of a fractional-order alcohol consumption model incorporating binge drinkers

In this work, by the use of Caputo–Fabrizio fractional derivative, the fractional-order Alcoholism addiction dynamics model is formulated which capture memory effects inherent in addiction-related processes. The well-posedness of the proposed model is established by showing the existence and uniqueness of solutions under some conditions which suits to the model. Furthermore, there is a demonstration of the positivity and boundedness of the model solutions by ensuring the biological feasibility of the system and Reproduction number and endemic equilibrium with sensitivity analysis and analysis of Phase plane and bifurcation system. To assess the robustness of the solutions with respect to small perturbations, The Ulam–Hyers stability of the fractional model is investigated. To obtain approximate solutions, A suitable numerical technique is employed, and numerical simulations are carried out using MATLAB to support the theoretical findings. The influence of different fractional orders on the system dynamics is observed, which shows the accelerating progression of Recovery. The graph highlights the significant role of memory effects. The fractional-order framework provides a more flexible and realistic description of addiction dynamics compared to the classical integer-order model. The results obtained offer qualitative insights for understanding behavioral patterns of the system.