Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters

M. M. El-Dessoky; Muhammad Altaf Khan

doi:10.3934/dcdss.2020429

Article Contents

2021, Volume 14, Issue 10: 3557-3575. Doi: 10.3934/dcdss.2020429

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Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters

M. M. El-Dessoky^1,2, and
Muhammad Altaf Khan^3, ,

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3.
Informetrics Research Group Ton Duc Thang University Ho Chi Minh City, Vietnam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City, Vietnam

^* Corresponding author: Muhammad Altaf Khan (muhammad.altaf.khan@tdtu.edu.vn)
^* Corresponding author: Muhammad Altaf Khan (muhammad.altaf.khan@tdtu.edu.vn)

Received: October 31, 2019

Revised: January 31, 2020

Early access: September 2020

Published: October 2021

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Abstract

The present work explore the dynamics of the cancer model with fractional derivative. The model is formulated in fractional type of Caputo-Fabrizio derivative. We analyze the chaotic behavior of the proposed model with the suggested parameters. Stability results for the fixed points are shown. A numerical scheme is implemented to obtain the graphical results in the sense of Caputo-Fabrizio derivative with various values of the fractional order parameter. Further, we show the graphical results in order to study that the model behave the periodic and quasi periodic limit cycles as well as chaotic behavior for the given set of parameters.

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Mathematics Subject Classification: Primary:26A33;Secondary:92J15.

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Figure 1. The plot shows the dynamics of the model (1), when $ \omega = 1 $

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Figure 2. The plot shows the dynamics of the model (1), when $ \omega = 0.95 $

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Figure 3. The plot shows the dynamics of the model (1), when $ \omega=0.9 $

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Figure 4. The plot shows the dynamics of the model (1), when $ \omega=0.85 $

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Figure 5. The plot shows the dynamics of the model (1), when $ \omega = 0.5 $

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Figure 6. The plot shows the dynamics of the model (1), when $ \omega = 1 $

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Figure 7. The plot shows the dynamics of the model (1), when $ \omega=0.9 $

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Figure 8. The plot shows the dynamics of the model (1), when $ \omega = 0.8 $

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Figure 9. The plot shows the dynamics of the model (1), when $ \omega = 1 $

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Figure 10. The plot shows the dynamics of the model (1), when $ \omega=0.9 $

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Figure 11. The plot shows the dynamics of the model (1), when $ h = 0.2 $ and $ \omega = 0.8 $

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