New numerical computation formula and error analysis of some existing formulae in fractional derivatives and integrals
Fractional calculus is non-integer calculus, and mainly used in engineering field. For instance, it is used for simulation of viscosity model or control system. This paper analyzes numerical computation formulae for calculating fractional derivatives and integrals. Those formulae are derived from Grunwald-Letkoniv de.nition. Two numerical computation formulae derived from Grunwald-Letkoniv de.nition have been suggested. One is theseemingly first order accuracy formula, and the other is the seemingly second order accuracy formula, but their orders were not proved. This paper veri.es the seemingly first order accuracy formula has actually first order accuracy, and disproves second order accuracy of the seemingly second order formula. In addition, this paper proposes a new formula with second order accuracy and verifies its order. The proposed numerical computation formulae derived from Grunwald-Letkoniv de.nition are easier to calculate than formulae derived from Riemann-Liouville definition, and have a property that they are extended version of Newton-Cotes rules and finite difference methods. Numerical computation formulae this paper verifies help deeper understandings of fractional calculus.
fractional derivatives fractional integrals finite difference method numerical methods error analysis Grunwald-Letkoniv definition
Yuki Takeuchi Reiji Suda
Department of Computer Science, Graduate School of InformationScience and Technology, The University Department of Computer Science, Graduate School of Information Science and Technology, The Universit
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-12
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）