A Physical Interpretation of Fractional Calculus and Fractional Calculus with Constant Extent of Integral

ZHANG Xu-xiu; QIU Tian-shuang; SHENG Hu

doi:10.3969/j.issn.0372-2112.2013.03.015

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A Physical Interpretation of Fractional Calculus and Fractional Calculus with Constant Extent of Integral

更新时间：2025-07-16

- A Physical Interpretation of Fractional Calculus and Fractional Calculus with Constant Extent of Integral
- Acta Electronica Sinica Vol. 41, Issue 3, Pages: 508-512(2013)
- 作者机构：
  
  1. 大连交通大学电气信息学院,辽宁,大连,116028
  2. 大连理工大学电子信息与电气工程学部,辽宁,大连,116024
  3. 大连交通大学电气信息学院,辽宁,大连,116028
  4. 大连理工大学电子信息与电气工程学部,辽宁,大连,116024
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2013.03.015
  CLC： TP14
- Published：2013
- 稿件说明：
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ZHANG Xu-xiu, QIU Tian-shuang, SHENG Hu. A Physical Interpretation of Fractional Calculus and Fractional Calculus with Constant Extent of Integral[J]. Acta Electronica Sinica, 2013, 41(3): 508-512.
DOI：

ZHANG Xu-xiu, QIU Tian-shuang, SHENG Hu. A Physical Interpretation of Fractional Calculus and Fractional Calculus with Constant Extent of Integral[J]. Acta Electronica Sinica, 2013, 41(3): 508-512. DOI： 10.3969/j.issn.0372-2112.2013.03.015.

摘要

本文讨论了现有的三种分数阶微积分基本定义(R-L(Riemann-Liouville)定义、G-L(Grumwald-Letnkov)定义和Caputo定义)对阶数的适用范围

以及三者之间的关系;强调指出分数阶导数与整数阶导数之间的区别.通过对分数阶微积分一个统一公式的讨论

以及给出分数阶微积分一个简单的物理解释

加深对分数阶微积分本质的认识;提出定域长分数阶微积分定义

给出它的直接数值算法

预期它可能在实践中得到应用.

Abstract

In this paper the order-range applied by fractional calculus R-L definition

G-L definition and Caputo definition along with the connections between above three definitions are discussed.The differences of fractional-order derivatives and integer-order derivatives are pointed out.An uniform formula of fractional-order integrals and derivatives along with a physical interpretation of fractional calculus are given.The definition of fractional calculus with constant extent of integral and its direct numerical value arithmetic are put forward

and its application is anticipated.

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