Optimal control of a fractional smoking system

In this paper, considering the contact transmission between heavy smokers and potential smokers, we propose a novel fractional smoking model. Moreover, introduce two intervention measures, i.e., media campaign adjuvant drug treatment, to model in order control spread of smoking. For controlled model, some important properties are discussed. Then, an optimal problem involving system. The existence for is also established. By applying calculus variation, derive necessary optimality conditions problem. Furthermore, develop numerical solution approach based on Adams-type predictor-corrector method solve derived Finally, results show that obtained strategies effective reducing susceptible individuals smokers.