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

Analytical and numerical validation for solving the fractional Klein-Gordon equation using the... Abstract In 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

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

Nonlinear Engineering , Volume 5 (3) – Sep 1, 2016

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
2192-8010
eISSN
2192-8029
DOI
10.1515/nleng-2016-0018
Publisher site
See Article on Publisher Site

Abstract

Abstract In 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.

Journal

Nonlinear Engineeringde Gruyter

Published: Sep 1, 2016

References