Abstract
Fractional velocity is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. The fractional velocity can be suitable for characterizing singular behavior of derivatives of Hölderian functions and non differentiable functions. Relations to integer-order derivatives and other integral-based definitions are discussed.It is demonstrated that for Hölder functions under certain conditions the product rules deviates from the Leibniz rule. This deviation is expressed by another quantity, fractional co-variation.
Acknowledgments
The work has been supported in part by a grant from Research Fund-Flanders (FWO), contract number 0880.212.840.
Reference
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