Fractional dynamical systems using the multistage generalized differential transform method

Abstract

In recent work, author in [1] employed the modified differential transform method(MDTM) for solving fractional Chen system. He derived numerical solutions by the MDTM with fractional order α = 0:99 and compared the results with ones obtained by the generalized Adams- Bashforth-Moulton method(GABMM), which is well know method for solving fractional problems. In this work, we show that MDTM does not give a reliable approximate solutions with a low order of fractional derivative. We analyse why the MDTM does not work well and propose the new multistage generalized differential transform method(MsGDTM) to overcome the difficulties arising in the MDTM. Illustrative examples show the performance of MsGDTM.