An Optimal Control Theory-Based Study for Fractional Smoking Model Using Bernoulli Wavelet Method

This paper introduces a dynamic model that explores smoking and optimal control strategies. It shows how fractional-order (FO) analysis has uncovered hidden parts of complex systems and provides information about previously ignored elements. This paper uses the Bernoulli wavelet operational matrix method and the Adam–Bashforth–Moulton (ABM) method to analyse this model numerically. The mathematical model is segmented into five sub-classes: susceptible smokers, ingestion class, unusual smokers, regular smokers, and ex-smokers. It considers four optimal control measures: an anti-smoking education campaign, distribution of anti-smoking gum, administration of anti-nicotine drugs, and governmental restrictions on smoking in public areas. We show in this model how to control smoking in society strategically.