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Adaptation of Differential Transform Method for the Numeric‐Analytic Solution of Fractional‐Order Rössler Chaotic and Hyperchaotic Systems

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  • Asad Freihat
  • Shaher Momani

Abstract

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.

Suggested Citation

  • Asad Freihat & Shaher Momani, 2012. "Adaptation of Differential Transform Method for the Numeric‐Analytic Solution of Fractional‐Order Rössler Chaotic and Hyperchaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:934219
    DOI: 10.1155/2012/934219
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    References listed on IDEAS

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    1. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
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    Cited by:

    1. Shih-Yu Li & Cheng-Hsiung Yang & Li-Wei Ko & Chin-Teng Lin & Zheng-Ming Ge, 2013. "Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time‐Reversed Uncertain Dynamical Systems′ Analysis and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Shih-Yu Li & Cheng-Hsiung Yang & Chin-Teng Lin & Li-Wei Ko & Tien-Ting Chiu, 2013. "Chaotic Motions in the Real Fuzzy Electronic Circuits," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Shaher Momani & Asad Freihat & Mohammed AL-Smadi, 2014. "Analytical Study of Fractional‐Order Multiple Chaotic FitzHugh‐Nagumo Neurons Model Using Multistep Generalized Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. S. S. Motsa & P. G. Dlamini & M. Khumalo, 2012. "Solving Hyperchaotic Systems Using the Spectral Relaxation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Ping Zhou & Rui Ding, 2012. "Modified Function Projective Synchronization between Different Dimension Fractional‐Order Chaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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