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Zbl 1237.37058
Freihat, Asad; Momani, Shaher
Adaptation of differential transform method for the numeric-analytic solution of fractional-order Rössler chaotic and hyperchaotic systems. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 934219, 13 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

Summary: 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.

MSC 2000:: *37M99 Approximation methods and numerical treatment of dynamical systems
37D45 Strange attractors, chaotic dynamics
65L06 Multistep, Runge-Kutta, and extrapolation methods
34A08

Keywords: generalized differential transform method (GDTM); fractional-order Rössler chaotic and hyperchaotic systems; Runge-Kutta method

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Zentralblatt MATH Berlin [Germany]