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Adaptation of differential transform method for the numeric-analytic solution of fractional-order Rössler chaotic and hyperchaotic systems. (English) Zbl 1237.37058
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:
37M99Approximation methods and numerical treatment of dynamical systems
37D45Strange attractors, chaotic dynamics
65L06Multistep, Runge-Kutta, and extrapolation methods
34A08Fractional differential equations