Mathematics and Computational Sciences

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

Document Type : Original Article

Authors

Rachid Belgacem 1
Ahmed Bokhari 1
Boualem Sadaoui 2

1 Laboratory of Mathematics and its Applications LMA, Hassiba Benbouali University of Chlef, Algeria.

2 Laboratory of Mathematics, Computer science and Applications, Djilali Bounaama University, Khemis Miliana, Algeria.

https://doi.org/10.30511/mcs.2026.2069397.1447
Abstract
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.

Keywords

Caputo fractional derivative
smoking model
Jafari integral transform
Homotopy Perturbation Method
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Mathematics and Computational Sciences
Volume 7, Issue 2
Spring 2026
Pages 106-124

  • Receive Date 19 August 2025
  • Revise Date 07 February 2026
  • Accept Date 21 February 2026

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