Study of HIV model via recent improved fractional differential and integral operators

Abd-Allah Hyder; Mohamed A. Barakat; Doaa Rizk; Rasool Shah; Kamsing Nonlaopon; Abd-Allah Hyder; Mohamed A. Barakat; Doaa Rizk; Rasool Shah; Kamsing Nonlaopon

doi:10.3934/math.2023084

AIMS Mathematics

2023, Volume 8, Issue 1: 1656-1671. doi: 10.3934/math.2023084

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Research article

Study of HIV model via recent improved fractional differential and integral operators

1.
Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha 61413, Saudi Arabia
2.
Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo 11371, Egypt
3.
Department of Computer Science, College of Al Wajh, University of Tabuk, Tabuk 71491, Saudi Arabia
4.
Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt
5.
Department of Mathematics, College of Science and Arts, Qassim University, Al-Asyah, Saudi Arabia
6.
Department of Mathematics, Abdul Wali khan university, Mardan 23200, Pakistan
7.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 28 August 2022 Revised: 01 October 2022 Accepted: 10 October 2022 Published: 24 October 2022
MSC : 26A33, 68Q07, 34E18

In this article, a new fractional mathematical model is presented to investigate the contagion of the human immunodeficiency virus (HIV). This model is constructed via recent improved fractional differential and integral operators. Other operators like Caputo, Riemann-Liouville, Katugampola, Jarad and Hadamard are being extended and generalized by these improved fractional differential and integral operators. Banach's and Leray-Schauder nonlinear alternative fixed point theorems are utilized to examine the existence and uniqueness results of the proposed fractional HIV model. Moreover, different kinds of Ulam stability for the fractional HIV model are established. It is simple to recognize that the extracted results can be reduced to some results acquired in multiple works of literature.
- human immunodeficiency virus,
- fractional mathematical modeling,
- fractional operators
Citation: Abd-Allah Hyder, Mohamed A. Barakat, Doaa Rizk, Rasool Shah, Kamsing Nonlaopon. Study of HIV model via recent improved fractional differential and integral operators[J]. AIMS Mathematics, 2023, 8(1): 1656-1671. doi: 10.3934/math.2023084

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Abstract

In this article, a new fractional mathematical model is presented to investigate the contagion of the human immunodeficiency virus (HIV). This model is constructed via recent improved fractional differential and integral operators. Other operators like Caputo, Riemann-Liouville, Katugampola, Jarad and Hadamard are being extended and generalized by these improved fractional differential and integral operators. Banach's and Leray-Schauder nonlinear alternative fixed point theorems are utilized to examine the existence and uniqueness results of the proposed fractional HIV model. Moreover, different kinds of Ulam stability for the fractional HIV model are established. It is simple to recognize that the extracted results can be reduced to some results acquired in multiple works of literature.

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