A study on the fractal-fractional tobacco smoking model

Hasib Khan; Jehad Alzabut; Anwar Shah; Sina Etemad; Shahram Rezapour; Choonkil Park; Hasib Khan; Jehad Alzabut; Anwar Shah; Sina Etemad; Shahram Rezapour; Choonkil Park

doi:10.3934/math.2022767

AIMS Mathematics

2022, Volume 7, Issue 8: 13887-13909. doi: 10.3934/math.2022767

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Research article

A study on the fractal-fractional tobacco smoking model

1.
Department of Mathematics, Shaheed Benazir Bhutto Uniersity, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
3.
Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Türkiye
4.
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
5.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
6.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
7.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 30 March 2022 Revised: 01 May 2022 Accepted: 08 May 2022 Published: 25 May 2022
MSC : 26A33, 34A08, 35R11

In this article, we consider a fractal-fractional tobacco mathematical model with generalized kernels of Mittag-Leffler functions for qualitative and numerical studies. From qualitative point of view, our study includes; existence criteria, uniqueness of solution and Hyers-Ulam stability. For the numerical aspect, we utilize Lagrange's interpolation polynomial and obtain a numerical scheme which is further illustrated simulations. Lastly, a comparative analysis is presented for different fractal and fractional orders. The numerical results are divided into four figures based on different fractal and fractional orders. We have found that the fractional and fractal orders have a significant impact on the dynamical behaviour of the model.
- fractal-fractional derivative,
- existence,
- tobacco model,
- stability,
- simulation,
- interpolation
Citation: Hasib Khan, Jehad Alzabut, Anwar Shah, Sina Etemad, Shahram Rezapour, Choonkil Park. A study on the fractal-fractional tobacco smoking model[J]. AIMS Mathematics, 2022, 7(8): 13887-13909. doi: 10.3934/math.2022767

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Abstract

In this article, we consider a fractal-fractional tobacco mathematical model with generalized kernels of Mittag-Leffler functions for qualitative and numerical studies. From qualitative point of view, our study includes; existence criteria, uniqueness of solution and Hyers-Ulam stability. For the numerical aspect, we utilize Lagrange's interpolation polynomial and obtain a numerical scheme which is further illustrated simulations. Lastly, a comparative analysis is presented for different fractal and fractional orders. The numerical results are divided into four figures based on different fractal and fractional orders. We have found that the fractional and fractal orders have a significant impact on the dynamical behaviour of the model.

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