The Numerical Differentiation Formulae for the Fractional Derivatives and the Truncation Error Estimates

机译：分数阶导数的数值微分公式和截断误差估计

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摘要

In this article, we will report some numerical differentiation formulae for the fractional derivatives and the truncation error estimates. L1 formula and shifted L1 formula for Caputo derivatives of order rγ(0 <γ<1) are established and the truncation errors are given brie.y. In addition, a formula for Caputo derivatives of order rγ (1 <γr<2) and the corresponding analysis of its truncation error are provided.

机译：在本文中，我们将报告一些分数导数和截断误差估计的数值微分公式。建立了阶次为rγ（0 <γ<1）的Caputo导数的L1公式和移位的L1公式，并给出了截断误差。此外，提供了rγ阶（1 <γr<2）的Caputo导数的公式以及其截断误差的相应分析。

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来源
《Proceedings of the Fifth symposium on fractional differentiation and its applications》|2012年|1-6|共6页
会议地点 Nanjing(CN)
作者
Zhi-zhong Sun; Guang-hua Gao;
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作者单位

Department of Mathematics, Southeast University, Nanjing 210096,P R China;

Department of Mathematics, Southeast University, Nanjing 210096, P R China;

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会议组织
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
numerical differentiation formulae; fractional derivative; truncation error; fractional differential equation; difference scheme;

机译：数值微分方程；分数导数；截断误差；分数微分方程；差分格式;

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The Numerical Differentiation Formulae for the Fractional Derivatives and the Truncation Error Estimates

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