K. M. Kolwankar
and 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”
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 F. Ben Adda
and 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.