Open Access

ARTICLE

Predictive and Global Effect of Active Smoker in Asthma Dynamics with Caputo Fractional Derivative

Muhammad Farman^1,2,3,*, Noreen Asghar⁴, Muhammad Umer Saleem⁴, Kottakkaran Sooppy Nisar^5,6, Kamyar Hosseini^1,2,7, Mohamed Hafez^8,9

1 Faculty of Arts and Sciences, Department of Mathematics, Near East University, TRNC, Mersin 10, Nicosia, 99138, Turkey
2 Research Center of Applied Mathematics, Khazar University, Baku, AZ-1096, Azerbaijan
3 Jadara University Research Center, Jadara University, Irbid, 21110, Jordan
4 Department of Mathematics, University of Education, Lahore, 54600, Pakistan
5 Department of Mathematics, College of Science and Humanities in Al Kharj, Prince Sattam bin Abdulaziz University, Al Kharj, 16277, Saudi Arabia
6 Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan
7 Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, 34959, Turkey
8 Faculty of Engineering and Quantity Surveying, INTI International University Colleges, Nilai, 71800, Malaysia
9 Faculty of Mangement, Shinawatra University, Pathum Thani, 12000, Thailand

* Corresponding Author: Muhammad Farman. Email:

(This article belongs to the Special Issue: Analytical and Numerical Solution of the Fractional Differential Equation)

Computer Modeling in Engineering & Sciences 2025, 145(1), 721-751. https://doi.org/10.32604/cmes.2025.069541

Received 25 June 2025; Accepted 03 September 2025; Issue published 30 October 2025

Abstract

Smoking is harmful to the lungs and has numerous effects on our bodies. This leads to decreased lung function, which increases the lungs’ susceptibility to asthma triggers. In this paper, we develop a new fractional-order model and investigate the impact of smoking on the progression of asthma by using the Caputo operator to analyze different factors. Using the Banach contraction principle, the existence and uniqueness of solutions are established, and the positivity and boundedness of the model are proved. The model further incorporates different stages of smoking to account for incubation periods and other latent effects, enhancing the accuracy of system dynamics. Within this Fractional operator framework, key analyses are performed, including the identification of equilibrium points, computation of the basic reproduction number, sensitivity analysis, and assessment of local and global stability with the Lyapunov function. Additionally, chaos stability employing linear response regulation is implemented mathematically, and the effect of the compartment shows through simulations. A numerical iterative method employing Newton polynomial interpolation is used to illustrate the effectiveness of the suggested model, and numerical simulations reveal its enhanced efficiency at various fractional orders. The fractional-order framework offers a more realistic representation than classical integer-order models.

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