Dynamic Modelling of Smoking Cessation with Caputo Fractional Derivatives: Incorporating Dual Quitter Behaviours
DOI:
https://doi.org/10.5890/DNC.2026.06.008Abstract
This study examines the dynamics of a smoking model using the Caputo ($\mathcal{C}$) fractional derivative, which effectively captures memory effects inherent in complex systems. We conduct a mathematical analysis of the fractional model, ensuring the positivity of solutions, invariant region and demonstrating the existence and uniqueness of solutions through fixed-point theory. For numerical simulations, we employ a generalized predictor-corrector method tailored for the $\mathcal{C}$ derivative. The model is computationally solved, and results are graphically illustrated across various fractional-order values.References
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