COMPARISON OF DIFFERENT NUMERICAL METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

The dynamical properties of fractional-order systems have attracted increasing attention in recent years. In this paper, numerical solutions of Chen system with fractional-order are given by using three different computational methods: Adams-Bashforth (FAB), Adams-Bashforth-Moulton (FABM) and Fractional Multistep Differential Transformation method (FMDTM). The fractional derivatives are described in the Caputo sense. Fractional FABM method acts like a predictor-corrector pair which represents an amalgamation between FAB and fractional Adams-Moulton (FAM) methods, and it is compared with FMDTM, which is a semi-numerical method that exploits the power series representation of the solution. The system is shown to display interesting dynamical behavior depending on the system parameters, such as a chaotic behavior, as well as stabilization towards regular periodic motion or equilibrium points. Numerically obtained results are analysed to compare various integration algorithms.