Some aspects of the numerical analysis of a fractional duffing oscillator with a fractional variable order derivative of the Riemann-Liouville type

In this paper, we consider some aspects of the numerical analysis mathematical model fractional Duffing with a derivative variable order Riemann-Liouville type. Using methods: an explicit finite-difference scheme based on Grunwald-Letnikov and Adams-Bashford-Moulton approximations (predictor-corrector), proposed is found. These methods have been verified test case. It shown that predictor-corrector method has faster convergence than according to scheme. For these schemes, using Runge's rule, estimates computational accuracy were made, which tended unity increase in number calculated grid nodes.