About non-differentiable functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:263

Article

Ben Adda, F ; Cresson, J

关键词: fractional calculus;    Riemann-Liouville fractional operators;    irregular functions;   

DOI  :  10.1006/jmaa.2001.7656

来源: Elsevier

【 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.

【 授权许可】

Free