An analytic study of the fractional order model of HIV-1 virus and CD4+ T-cells using adomian method

In this article, we study the fractional mathematical model of HIV-1 infection of CD4+ T-cells, by studying a system of fractional differential equations of first order with some initial conditions, we study the changing effect of many parameters. The fractional derivative is described in the caputo sense. The adomian decomposition method (Shortly, ADM) method was used to calculate an approximate solution for the system under study. The nonlinear term is dealt with the help of adomian polynomials. Numerical results are presented with graphical justifications to show the accuracy of the proposed methods.

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The Fractional Differential Model of HIV-1 Infection of CD4+T-Cells with Description of the Effect of Antiviral Drug Treatment

Computational and Mathematical Methods in Medicine ◽

10.1155/2019/4059549 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

Bijan Hasani Lichae ◽

Jafar Biazar ◽

Zainab Ayati

Keyword(s):

T Cells ◽

Fractional Order ◽

Fractional Derivatives ◽

Antiviral Drug ◽

Adomian Decomposition Method ◽

Differential Model ◽

Proposed Model ◽

Adomian Decomposition ◽

Fractional Differential ◽

Hiv 1

In this paper, the fractional-order differential model of HIV-1 infection of CD4+T-cells with the effect of drug therapy has been introduced. There are three components: uninfected CD4+T-cells,x, infected CD4+T-cells,y, and density of virions in plasma,z. The aim is to gain numerical solution of this fractional-order HIV-1 model by Laplace Adomian decomposition method (LADM). The solution of the proposed model has been achieved in a series form. Moreover, to illustrate the ability and efficiency of the proposed approach, the solution will be compared with the solutions of some other numerical methods. The Caputo sense has been used for fractional derivatives.

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Adomian Decomposition Method for Approximating the Solutions of the Bidirectional Sawada-Kotera Equation

Zeitschrift für Naturforschung A ◽

10.1515/zna-2010-8-906 ◽

2010 ◽

Vol 65 (8-9) ◽

pp. 658-664 ◽

Cited By ~ 2

Author(s):

Xian-Jing Lai ◽

Xiao-Ou Cai

Keyword(s):

Decomposition Method ◽

Initial Conditions ◽

Soliton Solutions ◽

Adomian Decomposition Method ◽

Nonlinear Problems ◽

Absolute Error ◽

Solitary Wave Solutions ◽

Adomian Polynomials ◽

Wave Solutions ◽

Adomian Decomposition

In this paper, the decomposition method is implemented for solving the bidirectional Sawada- Kotera (bSK) equation with two kinds of initial conditions. As a result, the Adomian polynomials have been calculated and the approximate and exact solutions of the bSK equation are obtained by means of Maple, such as solitary wave solutions, doubly-periodic solutions, two-soliton solutions. Moreover, we compare the approximate solution with the exact solution in a table and analyze the absolute error and the relative error. The results reported in this article provide further evidence of the usefulness of the Adomian decomposition method for obtaining solutions of nonlinear problems

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Dynamical Analysis of Approximate Solutions of HIV-1 Model with an Arbitrary Order

Complexity ◽

10.1155/2019/9715686 ◽

2019 ◽

Vol 2019 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Asma ◽

Nigar Ali ◽

Gul Zaman ◽

Anwar Zeb ◽

Vedat Suat Erturk ◽

...

Keyword(s):

Fractional Order ◽

Dynamical Behavior ◽

Adomian Decomposition Method ◽

Approximate Solutions ◽

Dynamical Analysis ◽

Order Model ◽

Hiv Model ◽

Fractional Order Model ◽

Adomian Decomposition ◽

Hiv 1

This article studies the dynamical behavior of the analytical solutions of the system of fraction order model of HIV-1 infection. For this purpose, first, the proposed integer order model is converted into fractional order model. Then, Laplace-Adomian decomposition method (L-ADM) is applied to solve this fractional order HIV model. Moreover, the convergence of this method is also discussed. It can be observed from the numerical solution that (L-ADM) is very simple and accurate to solve fraction order HIV model.

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A Novel Computational Technique for Impulsive Fractional Differential Equations

Symmetry ◽

10.3390/sym11020216 ◽

2019 ◽

Vol 11 (2) ◽

pp. 216 ◽

Cited By ~ 1

Author(s):

Changyou Ma

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Numerical Solutions ◽

Adomian Decomposition Method ◽

Computational Technique ◽

Adomian Polynomials ◽

Impulsive Fractional Differential Equations ◽

Approximate Analytical Solutions ◽

Adomian Decomposition ◽

Fractional Differential

A computational technique for impulsive fractional differential equations is proposed in this paper. Adomian decomposition method plays an efficient role for approximate analytical solutions for ordinary or fractional calculus. Semi-analytical method is proposed by use of the Adomian polynomials. The method successively updates the initial values and gives the numerical solutions on different impulsive intervals. As one of the numerical examples, an impulsive fractional logistic differential equation is given to illustrate the method.

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