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

Abstract EN

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.