Comparison of two numerical methods for fractional-order Rӧssler system

Abstract

In this paper, we numerically study the chaotic behavior of the fractional-order Rossler system comparing the numerical solutions of the system with Adams-Bashforth-Moulton method (FABM) and Fractional Multistep Differential Transformation method (FMDTM). The fractional derivatives are described in the Caputo sense. FABM method acts like a predictor-corrector pair compared with FMDTM, which is a semi-numerical method that exploits the power-series representation of the solution. Numerically obtained results are analyzed to compare the different integration algorithms. We quantify the distinction between the methods for arbitrary chosen system parameters in the chaotic regime. We have shown numerically that the difference between the results is less pronounced as the value of the fractional-order becomes closer to one.