scholarly journals The Numerical Investigation of Fractional-Order Zakharov–Kuznetsov Equations

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Pongsakorn Sunthrayuth ◽  
Farman Ali ◽  
A. A. Alderremy ◽  
Rasool Shah ◽  
Shaban Aly ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Numerical Investigation ◽  
Fractional Order ◽  
Decomposition Method ◽  
Suggested Method ◽  
Decomposition Technique ◽  
Modified Method ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Good Contact

In this article, a modified method called the Elzaki decomposition method has been applied to analyze time-fractional Zakharov–Kuznetsov equations. In this method, the Adomian decomposition technique and Elzaki transformation are combined. Two problems are investigated to show and validate the efficiency of the suggested method. It is also shown that the solutions achieved from the current producer are in good contact with the exact solutions to show with the help of graphs and table. It is observed that the suggested technique is to be reliable, efficient, and straightforward to implement for many related models of engineering and science.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

Modified Sumudu Decomposition Method for Solving Lane-Emden-Fowler Type Systems

2021 ◽  
Vol 20 ◽  
pp. 446-454
Author(s):  
Chokchai Viriyapong ◽  
Nongluk Viriyapong
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Type Systems ◽  
Singular Equations ◽  
Modified Method ◽  
Adomian Decomposition ◽  
Sumudu Transform

In this paper, the Sumudu decomposition method (SDM) is modified and applied to solve systems of singular equations of the Lane-Emden-Fowler type. The proposed method is based on the application of Sumudu transform and Adomian decomposition method. Some illustrative examples are given to demonstrate the efficiency of the proposed technique. The results show that the modified method is simple and effective

scholarly journals An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

scholarly journals The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 987 ◽  
Author(s):  
A. A. Alderremy ◽  
Hassan Khan ◽  
Rasool Shah ◽  
Shaban Aly ◽  
Dumitru Baleanu
Keyword(s):  
Mathematical Modeling ◽  
Analytical Solution ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Analytical Techniques ◽  
Whitham Equations ◽  
Suggested Technique ◽  
Approximate Analytical Solutions ◽  
Physical Phenomena

This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.

scholarly journals Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

2020 ◽  
Vol 52 (3) ◽  
pp. 339-352
Author(s):  
Omar Saber Qasim ◽  
Karam Adel Abed ◽  
Ahmed F. Qasim
Keyword(s):  
Exact Solutions ◽  
Hybrid Method ◽  
Decomposition Method ◽  
Firefly Algorithm ◽  
Fitness Function ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Optimal Parameters ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.

Exact Analytical Solution of Fractional Relaxation-Oscillation Equation by Adomian Decomposition and He’s Variational Technique

2009 ◽  
Author(s):  
K. C. Basak ◽  
P. C. Ray ◽  
R. K. Bera
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Decomposition Method ◽  
Exact Analytical Solution ◽  
Relaxation Oscillation ◽  
Variational Technique ◽  
Adomian Decomposition ◽  
Fractional Relaxation ◽  
Oscillation Equation

Exact solution of linear fractional relaxation-oscillation equation is obtained by the decomposition method of Adomian and also by He’s variational method for fractional order α, for 1 < α ≤ 2. Surface plots of the above solution are drawn for different values of fractional order α and time t. Amplitude of the oscillation increases with α but it decreases as time increases.

On Solution of Singular Integral Equations by Operator Method

2019 ◽  
Vol 14 ◽  
pp. 41-48
Author(s):  
Najem A. Mohammad ◽  
Mohammad Shami Hasso
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Operator Method ◽  
Singular Integral Equations ◽  
Transform Method ◽  
Suggested Technique ◽  
Adomian Decomposition

In this paper, we study the exact solution of singular integral equations using two methods, including Adomian Decomposition Method and Elzaki Transform Method. We propose an analytical method for solving singular integral equations and system of singular integral equations, and have some goals in our paper related to suggested technique for solving singular integral equations. The primary goal is for giving analytical solutions of such equations with simple steps, another goal is to compare the suggested method with other methods used in this study.

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