A Fractional Order Investigation of Smoking Model Using Caputo-Fabrizio Differential Operator

Abstract

Smoking is a social trend that is prevalent around the world, particularly in places of learning and at some significant events. The World Health Organization defines smoking as the most important preventable cause of disease and the third major cause of death in humans. In order to analyze this matter, this study typically emphasizes analyzing the dynamics of the fractional order quitting smoking model via the Caputo-Fabrizio differential operator. For the numerical solution of the considered model, the Laplace transform with the Adomian decomposition method (LADM) and Homotopy perturbation method (HPM) is applied, and the comparison of both the achieved numerical solutions is presented. Moreover, numerical simulation for the suggested scheme has been presented in various fractional orders with the aid of Matlab and the numerical results are supported by illustrative graphics. The simulation reveals the aptness of the considered model.

Keywords

• smoking model
• Caputo-Fabrizio fractional derivative
• Laplace transform
• Adomian decomposition method
• Homotopy perturbation method (HPM)
• numerical simulations