scholarly journals A General Iteration Formula of VIM for Fractional Heat- and Wave-Like Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Fukang Yin ◽  
Junqiang Song ◽  
Xiaoqun Cao
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Iteration Formula ◽  
Variational Iteration

A general iteration formula of variational iteration method (VIM) for fractional heat- and wave-like equations with variable coefficients is derived. Compared with previous work, the Lagrange multiplier of the method is identified in a more accurate way by employing Laplace’s transform of fractional order. The fractional derivative is considered in Jumarie’s sense. The results are more accurate than those obtained by classical VIM and the same as ADM. It is shown that the proposed iteration formula is efficient and simple.

scholarly journals Variational Iteration Method forq-Difference Equations of Second Order

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Guo-Cheng Wu
Keyword(s):  
Lagrange Multiplier ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Iteration Formula ◽  
Strongly Nonlinear ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Oscillation Equation

Recently, Liu extended He's variational iteration method to strongly nonlinearq-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. Theq-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.

scholarly journals Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem

2013 ◽  
Vol 17 (3) ◽  
pp. 715-721 ◽  
Author(s):  
Chun-Feng Liu ◽  
Shan-Shan Kong ◽  
Shu-Juan Yuan
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
Variational Iteration

A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals Variational Iteration Method for a Fractional-Order Brusselator System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Jafari ◽  
Abdelouahab Kadem ◽  
D. Baleanu
Keyword(s):  
Fractional Order ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Promising Tool ◽  
Approximate Analytical Solutions ◽  
Fractional Differential ◽  
Linear And Nonlinear

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.

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