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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/461837 |
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| author | C. Ünlü H. Jafari D. Baleanu |
| author_facet | C. Ünlü H. Jafari D. Baleanu |
| author_sort | C. Ünlü |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-096d24eaaf354cb59d7d92c8434b34d8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-096d24eaaf354cb59d7d92c8434b34d82025-02-03T01:24:27ZengWileyAbstract 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 |
| spellingShingle | C. Ünlü H. Jafari D. Baleanu Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2013/461837 |
| work_keys_str_mv | AT cunlu revisedvariationaliterationmethodforsolvingsystemsofnonlinearfractionalorderdifferentialequations AT hjafari revisedvariationaliterationmethodforsolvingsystemsofnonlinearfractionalorderdifferentialequations AT dbaleanu revisedvariationaliterationmethodforsolvingsystemsofnonlinearfractionalorderdifferentialequations |