University of Tabriz Computational Methods for Differential Equations 2345-3982 14 1 2026 11 01 A mathematical analysis of a non-linear smoking model via fractional operators 60 80 18762 10.22034/cmde.2024.62331.2738 EN Savita Panwar Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, India. Rupakshi Mishra Pandey Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, India. Sunil Dutt Purohit Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India. Shyamsunder - Department of Mathematics, SRM University Delhi-NCR, Sonepat-131029, Haryana, India. Journal Article 2024 07 03 Smoking is one of the most significant public health hazards that adversely affects all organs in the body and has a detrimental effect on general health. In this work, we investigate a mathematical smoking model by considering a singular and non-local Caputo operator as well as a non-singular modified Atangana-Baleanu Caputo derivative. We propose a Yang transform decomposition technique, which combines the Yang transform with the Adomian decomposition method, to obtain the analytical solution of the model. The existence of a unique solution to the model is established using the Lipschitz condition and fixed-point theory. The local asymptotic stability of the equilibrium point is also discussed. Furthermore, graphical analysis is carried out in order to demonstrate the impact of fractional order. https://cmde.tabrizu.ac.ir/article_18762_78c4a7fd529b6f3da0403bd7587d993f.pdf