Smoking dynamics with media awareness to control the prevalence of bad effect through fractional operator study.

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.