On calculus of local fractional derivatives
\textit{K. M. Kolwankar} and \textit{A. D. Gangal} [``Fractional differentiability of nowhere differentiable functions and dimensions'', Chaos 6, No.~4, 505-513 (1996; Zbl 1055.26504)] introduced a certain ``localization'' \(d^\alpha f(x)\) of the Riemann-Liouville fractional derivative to study the local behaviour of nowhere differentiable functions (see reviewer's remark on this notion in the review in Zbl to the paper by \textit{F. Ben Adda} and \textit{J. Cresson} [``About non-differentiable functions'', J. Math Anal. Appl. 263, No. 2, 721-737 (2001; Zbl 0995.26006)]). The authors study some properties of this ``localization'', such as the Leibniz rule for the product, the chain rule and others.
scientific article; zbMATH DE number 1801632