一类分形集的分数阶微积分  

Fractional Rank Calculus and Differential Coefficient of a Kind of Fractal Set

作　　者：潘学哉[1] 

机构地区：[1]南京师范大学泰州学院数学系,泰州225300

出　　处：《科学技术与工程》2010年第14期3439-3441,共3页Science Technology and Engineering

摘　　要：分形属于非线性科学,而构造分形集并用适当的方法对其进行研究是研究分形理论的重要手段之一。利用分数阶微积分的概念、性质对所构造的一类分形集(称之为康托m等份函数,设为Φ(x))的分析性质进行讨论,揭示了函数Φ(x)在一定条件下,在[0,1]上是几乎处处连续的、在[0,1]上存在ν阶分数阶积分和在[0,1]上几乎处处存在μ阶分数阶微分。Fractals belong to unline science,and creating fractals sets is one of ways through which study fractals theory.The thesis mainly discuss a new fractal set＇s（It is called Cantor m divided into equal parts function.）continuous property,monotone property,integrabel property and differentiability by applying the concept and properties of fraction rank calculous.It illustrates function Φ（x）.continous almost everywhere on[0,1];exists v-frc-tion rank calculous on[0,1] and exists fraction rank differential coedfficient almost everywhere[0,1].

关 键 词：分数阶积分 分数阶微分 康托m等份函数 

分 类 号：O189.12[理学—数学]