Analyzing Tobacco Smoking Dynamics: Fractional and Fractal-Fractional Approaches

This work aims to contribute insights into the dynamics of tobacco smoking models concerning snuffing users, and to assess the efficacy of different operators namely the Atangana-Baleanu fractional and fractal-fractional (FF) operators. We utilized fixed-point results to evaluate the existence and uniqueness of solutions for the model. Subsequently, we introduced a novel fractal-fractional concept by incorporating the AB fractional operator into the tobacco smoking model. Two numerical techniques are employed to address both the fractional and FF models. Graphical representations of numerical results are provided for the model encompassing a broad spectrum of fractional order values. Furthermore, we conducted a comparative analysis of the operators utilizing numerical schemes, accommodating diverse fractional order values.