Mathematical assessment of the dynamics of the tobacco smoking model: An application of fractional theory

Peijiang Liu; Taj Munir; Ting Cui; Anwarud Din; Peng Wu; Peijiang Liu; Taj Munir; Ting Cui; Anwarud Din; Peng Wu

doi:10.3934/math.2022398

AIMS Mathematics

2022, Volume 7, Issue 4: 7143-7165. doi: 10.3934/math.2022398

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Mathematical assessment of the dynamics of the tobacco smoking model: An application of fractional theory

1.
School of Statistics and Mathematics, Guangdong University of Finance and Economics, Big data and Educational Statistics Application Laboratory Guangzhou 510320, China
2.
School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
3.
Abdus Salam School of Mathematical Sciences GC University Lahore, 54600 Pakistan
4.
School of Economics, Guangdong University of Finance and Economics, Guangzhou 510320, China
5.
Department of Mathematics Sun Yat-sen University, Guangzhou 510275, China
6.
School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou 310018, China

Received: 28 October 2021 Revised: 16 January 2022 Accepted: 26 January 2022 Published: 09 February 2022
MSC : 46S40, 47H10, 54H25

In this paper we consider fractional-order mathematical model describing the spread of the smoking model in the sense of Caputo operator with tobacco in the form of snuffing. The threshold quantity $ \mathcal{R}_0 $ and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of of the solution of the considered model. The new version of numerical approximation's framework for the approximation of Caputo operator is used. Finally, the numerical results are presented to justify the significance of the arbitrary fractional order derivative. The analysis shows fractional-order model of tobacco smoking in Caputo sense gives useful information as compared to the classical integer order tobacco smoking model.
- fractional order model,
- tobacco smoking disease,
- Caputo fractional derivatives,
- fixed point theorem,
- numerical simulation
Citation: Peijiang Liu, Taj Munir, Ting Cui, Anwarud Din, Peng Wu. Mathematical assessment of the dynamics of the tobacco smoking model: An application of fractional theory[J]. AIMS Mathematics, 2022, 7(4): 7143-7165. doi: 10.3934/math.2022398

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Abstract

In this paper we consider fractional-order mathematical model describing the spread of the smoking model in the sense of Caputo operator with tobacco in the form of snuffing. The threshold quantity $ \mathcal{R}_0 $ and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of of the solution of the considered model. The new version of numerical approximation's framework for the approximation of Caputo operator is used. Finally, the numerical results are presented to justify the significance of the arbitrary fractional order derivative. The analysis shows fractional-order model of tobacco smoking in Caputo sense gives useful information as compared to the classical integer order tobacco smoking model.

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