scholarly journals New explicit solutions of the Klein–Gordon equation using the variational iteration method combined with the Exp-function method

2009 ◽  
Vol 58 (11-12) ◽  
pp. 2444-2448 ◽  
Author(s):  
Tong-ming Wang ◽  
Jia-min Zhu
Keyword(s):  
Iteration Method ◽  
Function Method ◽  
Gordon Equation ◽  
Variational Iteration Method ◽  
Explicit Solutions ◽  
Variational Iteration ◽  
Klein Gordon ◽  
Klein Gordon Equation

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.

Analytical and numerical validation for solving the fractional Klein-Gordon equation using the fractional complex transform and variational iteration methods

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
M. M. Khader ◽  
M. Adel
Keyword(s):  
Fractional Derivatives ◽  
Gordon Equation ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Variational Iteration ◽  
Klein Gordon ◽  
Iteration Methods ◽  
Order Four ◽  
Klein Gordon Equation

AbstractIn this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given.

scholarly journals Conformable fractional derivative and its application to fractional Klein-Gordon equation

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3745-3749
Author(s):  
Kangle Wang ◽  
Shaowen Yao
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Gordon Equation ◽  
Variational Iteration Method ◽  
Conformable Fractional Derivative ◽  
Fractional Complex Transform ◽  
Klein Gordon ◽  
Fractional Differential ◽  
Fractional Equation ◽  
Klein Gordon Equation

This paper adopts conformable fractional derivative to describe the fractional Klein-Gordon equations. The conformable fractional derivative is a new simple well-behaved definition. The fractional complex transform and variational iteration method are used to solve the fractional equation. The result shows that the proposed technology is very powerful and efficient for fractional differential equations.

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