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.

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

2021 ◽  
Vol 11 (2) ◽  
pp. 1460
Author(s):  
Kamel Al-Khaled ◽  
Maha Yousef
Keyword(s):  
T Cells ◽  
Cd4 T Cells ◽  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Order Model ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Adomian Method ◽  
Fractional Differential ◽  
Hiv 1

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.

scholarly journals Modeling the Dependence of Barometric Pressure with Altitude Using Caputo and Caputo–Fabrizio Fractional Derivatives

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yameni Noupoue Yannick ◽  
Kinda Abu Asbeh
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Error Rate ◽  
Fractional Derivatives ◽  
Classical Method ◽  
Main Tool ◽  
Barometric Pressure ◽  
Proposed Model ◽  
Fractional Differential ◽  
The Relationship

This work is dedicated to the study of the relationship between altitude and barometric atmospheric pressure. There is a consistent literature on this relationship, out of which an ordinary differential equation with initial value problems is often used for modeling. Here, we proposed a new modeling technique of the relationship using Caputo and Caputo–Fabrizio fractional differential equations. First, the proposed model is proven well-defined through existence and uniqueness of its solution. Caputo–Fabrizio fractional derivative is the main tool used throughout the proof. Then, follow experimental study using real world dataset. The experiment has revealed that the Caputo fractional derivative is the most appropriate tool for fitting the model, since it has produced the smallest error rate of 1.74% corresponding to the fractional order of derivative α  = 1.005. Caputo–Fabrizio was the second best since it yielded an error rate value of 1.97% for a fractional order of derivative α  = 1.042, and finally the classical method produced an error rate of 4.36%.

Solutions of the modified Kawahara equation with time-and space-fractional derivatives

2016 ◽  
Vol 7 (1) ◽  
pp. 10 ◽  
Author(s):  
M. Safavi ◽  
A. A. Khajehnasiri
Keyword(s):  
Approximate Solution ◽  
Fractional Differential Equations ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Time And Space ◽  
Kawahara Equation ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we consider fractional differential equations (FDEs), specially modified Kawahara equation with time and space fractional derivatives, also we use Adomian decomposition method (ADM) to approximate the exact solutions of this equation. The ADM method converts the FKEs to an iterated formula that approximate solution is computable. The numerical examples illustrate efficiency and accuracy of the proposed method.

scholarly journals Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Fazal Haq ◽  
Muhammad Shahzad ◽  
Shakoor Muhammad ◽  
Hafiz Abdul Wahab ◽  
Ghaus ur Rahman
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Epidemic Model ◽  
Adomian Decomposition Method ◽  
Classical Case ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
Fractional Differential

The fractional order Susceptible-Infected-Recovered (SIR) epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.

scholarly journals An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Moh’d Khier Al-Srihin ◽  
Mohammed Al-Refai
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
New Approach ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.

Multistage Adomian Decomposition Method for Solving NLP Problems Over a Nonlinear Fractional Dynamical System

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Decomposition Method ◽  
Optimization Problem ◽  
Adomian Decomposition Method ◽  
Optimal Solution ◽  
Initial Time ◽  
Adomian Decomposition ◽  
Fractional Differential ◽  
Fractional Dynamical System

This paper deals with implementation of the multistage Adomian decomposition method (MADM) to solve a class of nonlinear programming (NLP) problems, which are reformulated with a nonlinear system of fractional differential equations. The multistage strategy is used to investigate the relation between an equilibrium point of the fractional order dynamical system and an optimal solution of the NLP problem. The preference of the method lies in the fact that the multistage strategy gives this relation in an arbitrary longtime interval, while the Adomian decomposition method (ADM) gives the optimal solution just only in the neighborhood of the initial time. The numerical results taken by the fractional order MADM show that these results are compatible with the solution of NLP problem rather than the ADM. Furthermore, in some cases the fractional order MADM can perform more rapid convergency to the optimal solution of optimization problem than the integer order ones.

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 An Efficient Series Solution for Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mohammed Al-Refai ◽  
Mohamed Ali Hajji ◽  
Muhammad I. Syam
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Taylor Series Expansion ◽  
New Approach ◽  
Adomian Decomposition ◽  
Different Types ◽  
Fractional Differential

We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula, where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.

HYPERCHAOS IN THE FRACTIONAL-ORDER RÖSSLER SYSTEM WITH LOWEST-ORDER

2009 ◽  
Vol 19 (01) ◽  
pp. 339-347 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Point Of View ◽  
Hyperchaotic System ◽  
Adomian Decomposition ◽  
Rossler System ◽  
Fractional Differential ◽  
Rössler System

This Letter analyzes the hyperchaotic dynamics of the fractional-order Rössler system from a time-domain point of view. The approach exploits the Adomian decomposition method (ADM), which generates series solution of the fractional differential equations. A remarkable finding of the Letter is that hyperchaos occurs in the fractional Rössler system with order as low as 3.12. This represents the lowest order reported in literature for any hyperchaotic system studied so far.

scholarly journals Numerical Investigation of Chemical Schnakenberg Mathematical Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Faiz Muhammad Khan ◽  
Amjad Ali ◽  
Nawaf Hamadneh ◽  
Abdullah ◽  
Md Nur Alam
Keyword(s):  
Fractional Order ◽  
General Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Oscillatory Behavior ◽  
Biochemical Processes ◽  
Proposed Model ◽  
Adomian Decomposition ◽  
Schnakenberg Model ◽  
Caputo Differential Operator

Schnakenberg model is known as one of the influential model used in several biological processes. The proposed model is an autocatalytic reaction in nature that arises in various biological models. In such kind of reactions, the rate of reaction speeds up as the reaction proceeds. It is because when a product itself acts as a catalyst. In fact, model endows fractional derivatives that got great advancement in the investigation of mathematical modeling with memory effect. Therefore, in the present paper, the authors develop a scheme for the solution of fractional order Schnakenberg model. The proposed model describes an auto chemical reaction with possible oscillatory behavior which may have several applications in biological and biochemical processes. In this work, the authors generalized the concept of integer order Schnakenberg model to fractional order Schnakenberg model. We provided the approximate solution for the underlying generalized nonlinear Schnakenberg model in the sense of Caputo differential operator via Laplace Adomian decomposition method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by the aforementioned technique. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate techniques to handle nonlinear partial differential equations as compared to the other available numerical techniques. Finally, the obtained numerical solution is visualized graphically by MATLAB to describe the dynamics of desired solution.

Sign in / Sign up

Export Citation Format

Share Document