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

Author

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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, Hindawi, vol. 2012, pages 1-13, April.
    • Handle: RePEc:hin:jnlaaa:934219
    DOI: 10.1155/2012/934219
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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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