The LADM approach to analyze the fractional order model for smoking habits including memory

Abstract

Smoking is one of the leading causes of health issues, and it has several disastrous consequences. In this article, the solution of a mathematical model of smokers with a fractional derivative is discussed by the Laplace Adomian decomposition method (LADM). The proposed model's solution not only exists but is unique also. The suggested model is stable and dimensionally balanced. This article presents an analytical (approximate) solution for nonlinear fractional differential equations (FDEs) using the Caputo derivative. In addition, the model has provided relevant numerical and graphical descriptions. We also compare the results obtained from the LADM approach to the predictor-corrector method of the Adams-Bashforth-Moulton type.