Analysis of a fractional model for HIV CD$ 4^+ $ T-cells with treatment under generalized Caputo fractional derivative

Jutarat Kongson; Chatthai Thaiprayoon; Weerawat Sudsutad; Jutarat Kongson; Chatthai Thaiprayoon; Weerawat Sudsutad

doi:10.3934/math.2021427

AIMS Mathematics

2021, Volume 6, Issue 7: 7285-7304. doi: 10.3934/math.2021427

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Research article

Analysis of a fractional model for HIV CD$ 4^+ $ T-cells with treatment under generalized Caputo fractional derivative

1.
Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
2.
Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok 10400, Thailand
3.
Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 15 March 2021 Accepted: 26 April 2021 Published: 29 April 2021
MSC : 26A33, 34A08, 34A34, 34C60, 47H10

In this paper, a mathematical model of generalized fractional-order is constructed to study the problem of human immunodeficiency virus (HIV) infection of CD$ 4^+ $ T-cells with treatment. The model consists of a system of four nonlinear differential equations under the generalized Caputo fractional derivative sense. The existence results for the fractional-order HIV model are investigated via Banach's and Leray-Schauder nonlinear alternative fixed point theorems. Further, we also established different types of Ulam's stability results for the proposed model. The effective numerical scheme so-called predictor-corrector algorithm has been employed to analyze the approximated solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many discusses recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.
- fixed point theorems,
- generalized Caputo fractional derivative,
- mathematical model,
- predictor-corrector algorithm,
- Ulam-Hyers stability
Citation: Jutarat Kongson, Chatthai Thaiprayoon, Weerawat Sudsutad. Analysis of a fractional model for HIV CD$ 4^+ $ T-cells with treatment under generalized Caputo fractional derivative[J]. AIMS Mathematics, 2021, 6(7): 7285-7304. doi: 10.3934/math.2021427

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Abstract

In this paper, a mathematical model of generalized fractional-order is constructed to study the problem of human immunodeficiency virus (HIV) infection of CD$ 4^+ $ T-cells with treatment. The model consists of a system of four nonlinear differential equations under the generalized Caputo fractional derivative sense. The existence results for the fractional-order HIV model are investigated via Banach's and Leray-Schauder nonlinear alternative fixed point theorems. Further, we also established different types of Ulam's stability results for the proposed model. The effective numerical scheme so-called predictor-corrector algorithm has been employed to analyze the approximated solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many discusses recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.

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