  Singular functions and, in general, H\"older functions represent conceptual
models of nonlinear physical phenomena. The purpose of this survey is to
demonstrate the applicability of fractional velocity as a tool to characterize
Holder and in particular singular functions. Fractional velocities are defined
as limit of the difference quotient of a fractional power and they generalize
the local notion of a derivative. On the other hand, their properties contrast
some of the usual properties of derivatives. One of the most peculiar
properties of these operators is that the set of their non trivial values is
disconnected. This can be used for example to model instantaneous interactions,
for example Langevin dynamics. Examples are given by the De Rham and
Neidinger's functions, represented by iterative function systems. Finally the
conditions for equivalence with the Kolwankar-Gangal local fractional
derivative are investigated.
