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Analysis of a fractional model for HIV CD$ 4^+ $ T-cells with treatment under generalized Caputo fractional derivative
- Source :
- AIMS Mathematics, Vol 6, Iss 7, Pp 7285-7304 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
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.
- Subjects :
- ulam-hyers stability
General Mathematics
Human immunodeficiency virus (HIV)
Fixed-point theorem
Fractional model
medicine.disease_cause
Nonlinear differential equations
generalized caputo fractional derivative
fixed point theorems
Fractional calculus
predictor-corrector algorithm
Nonlinear system
Consistency (statistics)
Scheme (mathematics)
medicine
QA1-939
Applied mathematics
mathematical model
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 7
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....86df2ddae6b655e09ddcc656620d69ed