A mathematical analysis of a non-linear smoking model via fractional operators

Document Type : Research Paper

Authors

1 Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, India.

2 Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India.

3 Department of Mathematics, SRM University Delhi-NCR, Sonepat-131029, Haryana, India.

Abstract

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.

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Main Subjects

Computational Methods for Differential Equations
Volume 14, Issue 1
January 2026
Pages 60-80

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History

  • Receive Date: 03 July 2024
  • Revise Date: 20 October 2024
  • Accept Date: 29 October 2024

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