(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Over the past few years, several novel formulations of fractional derivatives have emerged, facilitating the construction of mathematical models that can address a broad spectrum of real-world applications. This study presents and investigates a mathematical model for smoking behavior incorporating the Caputo–Fabrizio fractional differential operator, which is par- ticularly valued for its non-singular kernel and ability to capture memory effects in dynamic systems without the complexities of singularities. Here, the population is divided into six distinct compartments: mainly susceptible, snuffing, irregular, habitual, regular, and quit. To explore the model’s dynamics, the Laplace Adomian Decomposition Method (LADM) and the Aboodh Adomian Decomposition Method (AADM) are employed. A comparative analysis of LADM and AADM is carried out using MATLAB software, with numerical simulations conducted for various fractional orders to assess the accuracy and efficiency of both techniques. Both methodologies demonstrated a high level of accuracy and consistency in their results, highlighting their reliability for modeling complex systems.