Oscillatory and complex behaviour of Caputo-Fabrizio fractional order HIV-1 infection model

Shabir Ahmad; Aman Ullah; Mohammad Partohaghighi; Sayed Saifullah; Ali Akgül; Fahd Jarad; Shabir Ahmad; Aman Ullah; Mohammad Partohaghighi; Sayed Saifullah; Ali Akgül; Fahd Jarad

doi:10.3934/math.2022265

AIMS Mathematics

2022, Volume 7, Issue 3: 4778-4792. doi: 10.3934/math.2022265

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Oscillatory and complex behaviour of Caputo-Fabrizio fractional order HIV-1 infection model

1.
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics, Clarkson University, New York, USA
3.
Art and Science Faculty, Department of Mathematics, Siirt University, TR-56100 Siirt, Turkey
4.
Department of Mathematics, Cankaya University, Etimesgut 06790, Ankara, Turkey
5.
King Abdulaziz University Jeddah, Saudi Arabia
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 02 December 2021 Revised: 20 December 2021 Accepted: 21 December 2021 Published: 27 December 2021
MSC : 92B05, 92C10

HIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.
- Picard iteration,
- fixed point theory,
- Caputo-Fabrizio derivative,
- chaotic behavior
Citation: Shabir Ahmad, Aman Ullah, Mohammad Partohaghighi, Sayed Saifullah, Ali Akgül, Fahd Jarad. Oscillatory and complex behaviour of Caputo-Fabrizio fractional order HIV-1 infection model[J]. AIMS Mathematics, 2022, 7(3): 4778-4792. doi: 10.3934/math.2022265

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Abstract

HIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.

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