Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations

Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations

A modification of the variational iteration method (VIM) for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE) obtained using the traditional variati...

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Main Authors: C. Ünlü, H. Jafari, D. Baleanu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/461837
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spelling doaj-096d24eaaf354cb59d7d92c8434b34d82020-11-24T23:07:45ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/461837461837Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential EquationsC. Ünlü0H. Jafari1D. Baleanu2Department of Mathematics, Faculty of Science, Istanbul University, Vezneciler, 34134 Istanbul, TurkeyInternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mmabatho 2735, South AfricaDepartment of Mathematics and Computer Science, Faculty of Arts and Sciences, Çankaya University, 06530 Ankara, TurkeyA modification of the variational iteration method (VIM) for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE) obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.http://dx.doi.org/10.1155/2013/461837
collection DOAJ
language English
format Article
sources DOAJ
author C. Ünlü
H. Jafari
D. Baleanu
spellingShingle C. Ünlü
H. Jafari
D. Baleanu
Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations
Abstract and Applied Analysis
author_facet C. Ünlü
H. Jafari
D. Baleanu
author_sort C. Ünlü
title Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations
title_short Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations
title_full Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations
title_fullStr Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations
title_full_unstemmed Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations
title_sort revised variational iteration method for solving systems of nonlinear fractional-order differential equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description A modification of the variational iteration method (VIM) for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE) obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.
url http://dx.doi.org/10.1155/2013/461837
work_keys_str_mv AT cunlu revisedvariationaliterationmethodforsolvingsystemsofnonlinearfractionalorderdifferentialequations
AT hjafari revisedvariationaliterationmethodforsolvingsystemsofnonlinearfractionalorderdifferentialequations
AT dbaleanu revisedvariationaliterationmethodforsolvingsystemsofnonlinearfractionalorderdifferentialequations
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