scholarly journals On the Fractional Nagumo Equation with Nonlinear Diffusion and Convection

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdon Atangana ◽  
Suares Clovis Oukouomi Noutchie
Keyword(s):  
Approximate Solution ◽  
Nonlinear Diffusion ◽  
Decomposition Method ◽  
Integral Transform ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Homotopy Decomposition ◽  
New Development ◽  
Nagumo Equation ◽  
Diffusion And Convection

We presented the Nagumo equation using the concept of fractional calculus. With the help of two analytical techniques including the homotopy decomposition method (HDM) and the new development of variational iteration method (NDVIM), we derived an approximate solution. Both methods use a basic idea of integral transform and are very simple to be used.

scholarly journals Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana ◽  
Adem Kılıçman
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Biharmonic Equations ◽  
Poisson Equations ◽  
Physical Problems ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
2D And 3D ◽  
Corrected Function

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as tends to infinity.

scholarly journals The Time-Fractional Coupled-Korteweg-de-Vries Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Aydin Secer
Keyword(s):  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
De Vries ◽  
Homotopy Analysis

We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).

scholarly journals On the Singular Perturbations for Fractional Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana
Keyword(s):  
Differential Equation ◽  
Singular Perturbation ◽  
Variational Iteration Method ◽  
Regular Perturbation ◽  
Homotopy Decomposition ◽  
New Development ◽  
The Laplace Transform ◽  
Nonhomogeneous Differential Equation ◽  
Fractional Differential ◽  
Linear Differential

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

scholarly journals Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 791 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Dian Chen Lu ◽  
Marjan Goodarzi
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transformation ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Integral Transform Method

This study is about the lubrication of a long porous slider in which the fluid is injected into the porous bottom. The similarity transformation reduces the Navier-Stokes equations to couple nonlinear, ordinary differential equations, which are solved by a new algorithm. The proposed technique is based on integral transformation. Apparently, there is great symmetry between proposed method and variation iteration method, Adomian decomposition method but in integral transform method all the boundary conditions are applied, then a recursive scheme is used for the analytical solutions, which is unlike the Variational Iteration Method, Adomian Decomposition Method, and other existing analytical methods. Solutions are obtained for much larger Reynolds numbers, and they are compared with analytical and numerical methods. Effects of Reynolds number on velocity components are presented.

scholarly journals A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1735
Author(s):  
Shuang-Shuang Zhou ◽  
Nehad Ali Shah ◽  
Ioannis Dassios ◽  
S. Saleem ◽  
Kamsing Nonlaopon
Keyword(s):  
Homotopy Perturbation Method ◽  
Graphical Representation ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Computational Techniques ◽  
System Of Nonlinear Equations ◽  
Gas Dynamics Equations ◽  
Homotopy Perturbation ◽  
Fractional System ◽  
Modified Forms

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

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