scholarly journals The multi-step homotopy analysis method for solving fractional-order model for HIV infection of CD4+T cells

2015 ◽  
Vol 34 (4) ◽  
pp. 307-322 ◽  
Author(s):  
AH H. Handam ◽  
Asad A. Freihat ◽  
M. Zurigat
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Cd4 T Cells ◽  
Analysis Method ◽  
Order Model ◽  
Fractional Order Model ◽  
Homotopy Analysis

scholarly journals Solving a fractional order model of HIV infection of CD4+ T cells

2011 ◽  
Vol 54 (9-10) ◽  
pp. 2132-2138 ◽  
Author(s):  
Ahmet Gökdoǧan ◽  
Ahmet Yildirim ◽  
Mehmet Merdan
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Fractional Order ◽  
Cd4 T Cells ◽  
Order Model ◽  
Fractional Order Model

scholarly journals A Method of Directly Defining the inverse Mapping for a HIV infection of CD4+ T-cells model

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mangalagama Dewasurendra ◽  
Ying Zhang ◽  
Noah Boyette ◽  
Ifte Islam ◽  
Kuppalapalle Vajravelu
Keyword(s):  
T Cells ◽  
Differential Equations ◽  
Hiv Infection ◽  
Cd4 T Cells ◽  
Applied Mathematics ◽  
Nonlinear Differential Equations ◽  
Cd4 T Cell ◽  
Analysis Method ◽  
Inverse Mapping ◽  
Homotopy Analysis

AbstractIn 2015, Shijun Liao introduced a new method of directly defining the inverse mapping (MDDiM) to approximate analytically a nonlinear differential equation. This method, based on the Homotopy Analysis Method (HAM) was proposed to reduce the time it takes in solving a nonlinear equation. Very recently, Dewasurendra, Baxter and Vajravelu (Applied Mathematics and Computation 339 (2018) 758–767) extended the method to a system of two nonlinear differential equations. In this paper, we extend it further to obtain the solution to a system of three nonlinear differential equations describing the HIV infection of CD4+ T-cells. In addition, we analyzed the advantages of MDDiM over HAM, in obtaining the numerical results. From these results, we noticed that the infected CD4+ T-cell density increases with the number of virions N; but decreases with the blanket death rate μI.

An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag–Leffler Kernel

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Order Model ◽  
Science And Engineering ◽  
Transform Method ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis

Abstract In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method (q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag–Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.

scholarly journals Homotopy Analysis Method for a Fractional Order Equation with Dirichlet and Non-Local Integral Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1167
Author(s):  
Said Mesloub ◽  
Saleem Obaidat
Keyword(s):  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Initial Boundary Value

The main purpose of this paper is to obtain some numerical results via the homotopy analysis method for an initial-boundary value problem for a fractional order diffusion equation with a non-local constraint of integral type. Some examples are provided to illustrate the efficiency of the homotopy analysis method (HAM) in solving non-local time-fractional order initial-boundary value problems. We also give some improvements for the proof of the existence and uniqueness of the solution in a fractional Sobolev space.

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