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.
