# American Institute of Mathematical Sciences

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

 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

Received  November 2019 Revised  February 2020 Early access  September 2020

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.

Citation: M. M. El-Dessoky, Muhammad Altaf Khan. Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020429
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The plot shows the dynamics of the model (1), when $\omega = 1$
The plot shows the dynamics of the model (1), when $\omega = 0.95$
The plot shows the dynamics of the model (1), when $\omega=0.9$
The plot shows the dynamics of the model (1), when $\omega=0.85$
The plot shows the dynamics of the model (1), when $\omega = 0.5$
The plot shows the dynamics of the model (1), when $\omega = 1$
The plot shows the dynamics of the model (1), when $\omega=0.9$
The plot shows the dynamics of the model (1), when $\omega = 0.8$
The plot shows the dynamics of the model (1), when $\omega = 1$
The plot shows the dynamics of the model (1), when $\omega=0.9$
The plot shows the dynamics of the model (1), when $h = 0.2$ and $\omega = 0.8$
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