A new computational strategy for solving a fractional-order smoking epidemic model

This study aims to investigate a fractional-order mathematical model that describes smoking behavior, formulated using the Caputo fractional (CF) derivative. which effectively captures long-term memory effects the population is divided into five compartments: potential smokers, current smokers, occasional smokers, permanent quitters, and temporary quitters. The model incorporates several parameters characterizing transition rates between these compartments, allowing for a realistic simulation of smoking dynamics. To obtain efficient approximate solutions, we present a new hybrid approach, both analytical and numerical, which combines the specific general integral transform with the homotopy perturbation method (HPM). Numerical simulations performed in MATLAB for different fractional orders reveal the high precision and numerical performance of the proposed technique. Graphical analyses further highlight the method’s effectiveness in capturing the temporal evolution of the model, confirming the reliability of the hybrid approach in representing such complex dynamical systems.

کلیدواژه ها:

Caputo fractional derivative ، smoking model ، Jafari integral transform ، Homotopy Perturbation Method