Analysis and Simulation of Fractional Order Smoking Epidemic Model.

Authors :: Ahmad A
Farman M
Ghafar A
Inc M
Ahmad MO
Sene N
Source :: Computational and mathematical methods in medicine [Comput Math Methods Med] 2022 May 20; Vol. 2022, pp. 9683187. Date of Electronic Publication: 2022 May 20 (Print Publication: 2022).
Publication Year :: 2022
Abstract: In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were established to overcome the various real-life problems. The true purpose of the current work is to develop and analyze Atangana-Baleanu (AB) with Mittag-Leffler kernel and Atangana-Toufik method (ATM) of fractional derivative model for the Smoking epidemic. Qualitative analysis has been made to `verify the steady state. Stability analysis has been made using self-mapping and Banach space as well as fractional system is analyzed locally and globally by using first derivative of Lyapunov. Also derive a unique solution for fractional-order model which is a new approach for such type of biological models. A few numerical simulations are done by using the given method of fractional order to explain and support the theoretical results.<br />Competing Interests: The authors state that there is no conflict of interest.<br /> (Copyright © 2022 Aqeel Ahmad et al.)