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Physical and Geometrical Interpretation of Grünwald-Letnikov Differintegrals: Measurement of Path and Acceleration

  • Radosław Cioć EMAIL logo


A function f(t) of the independent variable t changing with every increment dt can be formulated as a functional sequence. If g(f(t)) is a derivative or an integral of f(t) and the value of dt is interpreted subject to an error ΔT, then g(f(t)) is Grünwald-Letnikov differintegral of that sequence with an order closely related to dt and ΔT. This paper illustrates this relationship and proposes a geometrical and physical interpretation of a fractional order Grünwald-Letnikov differintegrals using the example of path and acceleration measurements of a point in motion.


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  1. Please cite to this paper as published in:

    Fract. Calc. Appl. Anal., Vol. 19, No 1 (2016), pp. 161–172, DOI: 10.1515/fca-2016-0009

Received: 2015-1-16
Revised: 2015-11-20
Published Online: 2016-3-9
Published in Print: 2016-2-1

#x00A9; 2016 Diogenes Co., Sofia

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