On the fractal-fractional modelling of the smoking problem

The tobacco epidemic is an example of the most significant common health peril the world has ever suffered. Cancer-related lung throat and heart disease are the principal warnings because of smoking. The importance of this problem motivated us to model it in the frame of fractal fractional derivative. We use Atangana-Baleanu-Caputo operator. Moreover, to confirm that there is a solution for the proposed model, we apply the theorems of Schauder fixed point and Banach fixed. Also, to obtain the numerical solutions of the offered model Atangana-Toufik technique is applied. To show the performance of the used method for the considered problem, different values of fractal and fractional orders are chosen. Additionally, successful graphs of solutions are provided for each case.