Numerical Treatment for the Caputo-Fabrizio Fractional Smoking Model using an Efficient Numerical Technique

Abstract

Smoking is a prevalent social behavior widely practiced worldwide, especially in settings such as schools and some significant gatherings. Based on the World Health Organization (WHO), smoking is the third leading source of human mortality and the primary preventable cause of disease. This study introduces a highly efficient simulation technique to analyze and solve the Caputo-Fabrizio (CF) fractional smoking model. We numerically solve the fractional integral equations (FIEs) with Simpson’s 1/3 rule, an effective numerical integration technique. We concentrate on clarifying the stability/convergence of the proposed strategy. We juxtapose the outcomes derived using the Runge-Kutta method (RK4) with those obtained through the implemented methodology. The findings indicate that the used technique provides a simple and efficient instrument for simulating the solution of these models. The principal advantage of the proposed method is its dependence on a limited number of straightforward steps, devoid of long-term consequences or reliance on a perturbation parameter.