About non-differentiable functions

被引：93

作者：

Ben Adda, F

Cresson, J

机构：

[1] Univ Paris 06, Lab Anal Numer, F-75013 Paris, France

[2] Besancon Univ Franche Comte, Equipe Math, F-25030 Besancon, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2001年 / 263卷 / 02期

关键词：

fractional calculus; Riemann-Liouville fractional operators; irregular functions;

D O I：

10.1006/jmaa.2001.7656

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop the notion of local fractional derivative introduced by Kolvankar and Gangal. It allows a fine study of the local structure of irregular (fractal) functions. Using this tool, we extend classical theorems of analysis (extrema, Rolle) to non-differentiable functions. In particular, we prove a generalized Taylor expansion theorem. We introduce a new derivative of real order and discuss its properties. (C) 2001 Academic Press.

引用

页码：721 / 737

页数：17

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