Analytical Study of a Fractional Smoking Epidemic Model: A Comparative Study via Yang–Abdel–Cattani and Atangana–Baleanu Derivative with Sumudu Transform

This study presents an analytical method based on the Sumudu transform decomposition method to find an approximate solution for a fractional smoking epidemic model. In this work, fractional derivatives have been taken in the sense of the Yang–Abdel–Cattani operator along with the Atangana–Baleanu derivative in the Caputo sense. A model is developed to explain smoking behavior among adults, which is still a serious health problem worldwide. A nonlinear system is used to study how smoking habit changes with time and how it affects populations. Existence and uniquessness are also derived to show the validity of the approach used. The method applied is simple, stable, and efficient for solving nonlinear fractional epidemic models. Results of the model show that the current model describes the problem in the best possible way and how smoking impacts the population.