About Non-differentiable Functions

✍ Scribed by Fayçal Ben Adda; Jacky Cresson

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 134 KB
• Volume: 263
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7656

✦ Synopsis

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.