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

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
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.

scholarly journals Numerical, Approximate Solutions, and Optimal Control on the Deathly Lassa Hemorrhagic Fever Disease in Pregnant Women

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. Higazy ◽  
A. El-Mesady ◽  
A. M. S. Mahdy ◽  
Sami Ullah ◽  
A. Al-Ghamdi
Keyword(s):  
Optimal Control ◽  
Pregnant Women ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Hemorrhagic Fever ◽  
Approximate Solutions ◽  
Order Model ◽  
Fractional Order Model ◽  
Adomian Decomposition ◽  
Negative Impacts

This paper is devoted to the model of Lassa hemorrhagic fever (LHF) disease in pregnant women. This disease is a biocidal fever and epidemic. LHF disease in pregnant women has negative impacts that were initially appeared in Africa. In the present study, we find an approximate solution to the fractional-order model that describes the fatal LHF disease. Laplace transforms coupled with the Adomian decomposition method (ADM) are applied. In addition, the fractional-order LHF model is numerically simulated in terms of a varied fractional order. Furthermore, a fractional order optimal control for the LHF model is studied.

Implementation of fractional optimal control problems in real-world applications

2020 ◽  
Vol 23 (6) ◽  
pp. 1783-1796
Author(s):  
Neelam Singha
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Order Model ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Real World Applications ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order model describes the interaction of effector-immune cells and tumor cells, including combined chemo-immunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractional-order optimal control problem. The key motive is to perform numerical simulations that shall facilitate us in understanding the behavior of state and control variables. Further, the graphical interpretation of solutions effectively validates the applicability of the present analysis to investigate the growth of cancer cells in the presence of medical treatment.

scholarly journals Dynamical analysis of fractional order model of immunogenic tumors

2016 ◽  
Vol 8 (7) ◽  
pp. 168781401665670 ◽  
Author(s):  
Sadia Arshad ◽  
Dumitru Baleanu ◽  
Jianfei Huang ◽  
Yifa Tang ◽  
Maysaa Mohamed Al Qurashi
Keyword(s):  
Fractional Order ◽  
Dynamical Analysis ◽  
Order Model ◽  
Fractional Order Model

A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients

2014 ◽  
Vol 07 (04) ◽  
pp. 1450036 ◽  
Author(s):  
A. A. M. Arafa ◽  
S. Z. Rida ◽  
M. Khalil
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Real Data ◽  
Euler Method ◽  
Order Model ◽  
Fractional Order Model ◽  
Plasma Virus Load ◽  
Hiv 1

In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.

scholarly journals A New Computational Approach for Solving Fractional Order Telegraph Equations

2021 ◽  
Vol 13 (3) ◽  
pp. 715-732
Author(s):  
A. Devi ◽  
M. Jakhar
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Computational Approach ◽  
Order Problem ◽  
Adomian Decomposition ◽  
Telegraph Equations ◽  
Derivatives Of

In this work, a modified decomposition method namely Sumudu-Adomian Decomposition Method (SADM) is implemented to find the exact and approximate solutions of fractional order telegraph equations. The derivatives of fractional-order are expressed in terms of caputo operator. Some numerical examples are illustrated to examine the efficiency of the proposed technique. Solutions of fractional order telegraph equations are obtained in the form of a series solution. It is observed that the solutions of fractional order telegraph equations converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested method.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
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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