A COMPREHENSIVE ANALYSIS AND OPTIMAL CONTROL FOR A NONLINEAR (φ1,φ2)-FRACTIONAL DIFFERENTIAL EQUATIONS TOXIC DRINKS MODEL PERTAINING TO MITTAG-LEFFLER KERNEL TECHNIQUES

This research examines a novel type of numerical analysis by presenting a six-cohort system of differential equations with regard to newly developed [Formula: see text] derivative operators. The framework’s qualitative aspect, as well as its basic features and fundamental reproductive quantity [Formula: see text], are investigated. Furthermore, we assess the sensitivity of parameter estimation in order to identify the specifications that have a significant impact on the reproducing quantity [Formula: see text]. The steady-state analysis of the system revealed that the framework is asymptotically stable both locally and globally at the beverage-free steady state [Formula: see text] when [Formula: see text]. Additionally, we emphasize the significance of therapies within alcoholism rehabilitation facilities, including the goal of determining the best methodologies for reducing the number of alcoholics while boosting the number of massive alcoholics who access addictive personality therapeutic centers. We classify these optimized constraints using Pontryagin’s maximum concept in the discrete domain. For the initial moment, we create a framework for quitting toxic beverages in order to analyze their nonlinear dynamic behaviors by taking into account two specifications of certain generalized operators: fractional-order [Formula: see text] and fractal-dimension [Formula: see text] To evaluate the existence of solutions, we employ a special classification of non-decreasing mappings. A simplified scheme predicated on the Lipschitz assumption is used to deduce the uniqueness criteria. Ultimately, we employ numerical methods and figures generated by Lagrangian piece-wise interpolation to exemplify all the approximated results and conclusions, and we communicate all behaviors of the appropriate interventions in the fractal–fractional mechanism. As a consequence, the acquired findings corroborate the optimal control scheme’s effectiveness.