Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives

2006 ◽  
Vol 47 (8) ◽  
pp. 082902 ◽  
Author(s):  
G. E. Drăgănescu
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Viscoelastic Models ◽  
Variational Iteration ◽  
Nonlinear Viscoelastic ◽  
Linear And Nonlinear

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.

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

scholarly journals Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li Chen ◽  
Yang Zhao ◽  
Hossein Jafari ◽  
J. A. Tenreiro Machado ◽  
Xiao-Jun Yang
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Mathematical Physics ◽  
Nondifferentiable Functions ◽  
Independent Variables ◽  
Poisson Equations ◽  
Variational Iteration ◽  
Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Numerical solution of the general Volterra nth-order integro-differential equations via variational iteration method

2018 ◽  
Vol 13 (02) ◽  
pp. 2050042
Author(s):  
Fernane Khaireddine
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
General Formula ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Linear And Nonlinear

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general [Formula: see text]th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Porous Medium ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Scientific Models ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Variational Iteration ◽  
Hybrid Selection ◽  
Linear And Nonlinear

AbstractWe apply the variational iteration method (VIM) for solving linear and nonlinear ordinary differential equations with variable coefficients. We use distinct Lagrange multiplier for each order of ODE. We emphasize the power of the method by testing a variety of models with distinct orders and variable coefficients. Scientific models, namely, the hybrid selection model, the Thomas-Fermi equation, the Kidder equation of the Unsteady flow of gas through a porous medium, and the Riccati equation, are studied as well.

scholarly journals Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Iteration Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Variational Iteration

We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.

scholarly journals Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Financial Models ◽  
Gordon Equation ◽  
Burgers Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Liouville Derivative ◽  
Black Scholes ◽  
Klein Gordon

We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense. To show the efficiency of the considered method, some examples that include the fractional Klein-Gordon equation, fractional Burgers equation, and fractional Black-Scholes equation are investigated.

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