ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Dynamical Behavior and Mathematical Analysis of Fractional Order Smoking Model

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 57--74 | DOI:10.5890/DNC.2023.03.005

Aqeel Ahmad$^1$, Muhammad Farman$^2$, Ali Akgul$^3$, Adnan Khan$^4$

Abstract

In this paper the fractional order smoking model is represent with Caputo and Caputo Fabrizio fractional derivative operator of order $\phi \in (0, 1]$ for dynamical transmission of smoking. Human beings face dangerous diseases caused by smoking, including arms, lungs, stomach, cervix, breast, pancreatic cancer and many others. Stability and qualitative analysis of model is studied to show the dynamical behaviour of the model in feasible region. It's important to note that a more powerful approach for computing convergent solutions is applied for mathematical models based on a fractional order differential equation structure. Study of the convergence is often provided to demonstrate the process's effectiveness. It shows the stability, uniqueness and applicability of the model for the control of smoking in the society. Numerical simulation are established to show the actual behavior of the smoking spread.

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