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