分数阶微积分的一种物理解释和定域长分数阶微积分  

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

作　　者：张旭秀[1,2] 邱天爽[2] 盛虎[1] 

机构地区：[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

出　　处：《电子学报》2013年第3期508-512,共5页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61003175/F020504;No.61201419);中国博士后科学基金(No.20080441121);辽宁省自然科学基金(No.20112015)

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.In this paper the order-range applied by fractional calculus R-L definition, G-L definition and Caputo definition a- long 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.

关 键 词：分数阶微积分R-L定义 分数阶微积分G-L定义 分数阶微积分Caputo定义 分数阶微积分的物理解释 定域长分数阶微积分 

分 类 号：TP14[自动化与计算机技术—控制理论与控制工程]