Using Modified Fractional Euler Formula for Solving the Fractional Smoking Model

Abstract

Worldwide, smoking is a common social practice, especially in places like schools and on important occasions. World Health Organization (WHO) states that smoking is the thirdleading cause of death worldwide and the most significant avoidable reason for disease. So, this work is devoted to giving a numerical simulation of the smoking model in its fractional form
(Liouville-Caputo sense). The novel numerical scheme used is the modified fractional Euler method (MFEM). We compare the given technique with the traditional fractional Euler method. In the hope of providing some recommendations to reduce the risks of this bad behavior, the effect of some parameters and external factors affecting the solution behavior of this proposed mathematical model was studied, including the recruitment rate (due to immigration or birth) and the smoking cessation rate. The results confirm the implemented scheme is a straightforward and efficient tool for obtaining solutions to these problems.