A Numerical Algorithm of Discrete Fractional Calculus by using Inhomogeneous Sampling Data

Abstract

This paper presents an efficient numerical method to realize discrete models of fractional derivatives and inte-grals which imply derivatives and integrals of arbitrary real order. This approach is based on a class of Stieltjes integrals transferred from the Riemann-Liouville definition. It is to calculate on inhomogeneous sampling periods which are getting longer as the operation points go back toward the initial time. It leads to the effective quality which has low computational costs and enough accuracy. The calculation times and precision of the proposed procedure are compared with those of a conventional procedure for a practical numerical simulation and the effectiveness of this procedure is verified.