Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems
A new reliable algorithm based on an adaptation of the standard generalized differential transform method (GDTM) is presented. The GDTM is treated as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of fractional-order Rössler chaotic and hypercha...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/934219 |
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| _version_ | 1832564404421394432 |
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| author | Asad Freihat Shaher Momani |
| author_facet | Asad Freihat Shaher Momani |
| author_sort | Asad Freihat |
| collection | DOAJ |
| description | A new reliable algorithm based on an adaptation of the standard generalized differential transform method (GDTM) is presented. The GDTM is treated as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of fractional-order Rössler chaotic and hyperchaotic systems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus. |
| format | Article |
| id | doaj-art-5e7db0d1ce454b279153a9448312158b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5e7db0d1ce454b279153a9448312158b2025-02-03T01:11:04ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/934219934219Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic SystemsAsad Freihat0Shaher Momani1Department of Mathematics, Faculty of Science, The University of Jordan, Amman 1194, JordanDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman 1194, JordanA new reliable algorithm based on an adaptation of the standard generalized differential transform method (GDTM) is presented. The GDTM is treated as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of fractional-order Rössler chaotic and hyperchaotic systems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.http://dx.doi.org/10.1155/2012/934219 |
| spellingShingle | Asad Freihat Shaher Momani Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems Abstract and Applied Analysis |
| title | Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems |
| title_full | Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems |
| title_fullStr | Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems |
| title_full_unstemmed | Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems |
| title_short | Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems |
| title_sort | adaptation of differential transform method for the numeric analytic solution of fractional order rossler chaotic and hyperchaotic systems |
| url | http://dx.doi.org/10.1155/2012/934219 |
| work_keys_str_mv | AT asadfreihat adaptationofdifferentialtransformmethodforthenumericanalyticsolutionoffractionalorderrosslerchaoticandhyperchaoticsystems AT shahermomani adaptationofdifferentialtransformmethodforthenumericanalyticsolutionoffractionalorderrosslerchaoticandhyperchaoticsystems |