  The paper demonstrates the basic properties of the local fractional variation
operators (termed fractal variation operators). The action of the operators is
demonstrated for local characterization of Holderian functions. In particular,
it is established that a class of such functions exhibits singular behavior
under the action of fractal variation operators in infinitesimal limit. The
link between the limit of the fractal variation of a function and its
derivative is demonstrated. The paper presents a number of examples, including
the calculation of the fractional variation of Cauchy sequences leading to the
Dirac's delta-function.
