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Some Applications of Fractional Velocities

  • Dimiter Prodanov EMAIL logo


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.


The work has been supported in part by a grant from Research Fund-Flanders (FWO), contract number 0880.212.840.


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Received: 2015-2-11
Revised: 2015-12-1
Published Online: 2016-3-9
Published in Print: 2016-2-1

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