Farman, Muhammad and Alfiniyah, Cicik and Jamil, Khadija and Sambas, Aceng and Millah, Nashrul and Ahmadin (2025) Smoking dynamics with media awareness to control the prevalence of bad effect through fractional operator study. MethodsX, 15.

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Abstract

Smoking remains a persistent global health concern with complex behavioral dynamics influenced by memory and past experiences. This study formulates and analyses a fractional-order mathematical model of smoking behavior using the Caputo derivative to capture memory effects and non-local interactions. The well-posedness of the model is ensured through rigorous proofs of existence and uniqueness of solutions. To assess the system’s resilience, Hyers-Ulam-Rassias stability is investigated under small perturbations. To address potential chaotic behavior, we implement chaos control techniques, stabilizing the system for reliable long-term predictions. A novel Newton polynomial-based numerical scheme is developed to efficiently approximate solutions, validated through extensive simulations. Our results demonstrate that fractional-order modeling provides deeper insights into smoking dynamics compared to classical approaches. Some key features of the proposed method include: • Investigating Hyers-Ulam-Rassias stability to analyze robustness against perturbations. • Applying chaos control techniques to manage and stabilize chaotic system behavior. • Developing and implementing a Newton polynomial-based numerical scheme for efficient solution approximation

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