Measuring Functions Smoothness with Local Fractional Derivatives

Kiran M. Kolwankar (1) , Jacques Lévy Véhel (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 FRACTALES - Fractals, complex models and artificial evolution

We study a notion of local fractional differentiation, obtained by localizing the classical fractional derivative. We show that it is strongly related with the local Hölder exponent, and give an interpretation of this result in terms of 2-microlocal analysis.

Domaines: Probabilités [math.PR]

Kiran M. Kolwankar, Jacques Lévy Véhel. Measuring Functions Smoothness with Local Fractional Derivatives. Fractional Calculus and Applied Analysis, 2001, 4 (3), pp.285-301. ⟨inria-00578645⟩