Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Mathematical Description of Elastic Phenomena which Uses Caputo or Riemann-Liouville Fractional Order Partial Derivatives is Nonobjective

Version 1 : Received: 6 August 2020 / Approved: 7 August 2020 / Online: 7 August 2020 (11:43:01 CEST)

How to cite: Balint, A.M.; Balint, S.; Birauas, S. Mathematical Description of Elastic Phenomena which Uses Caputo or Riemann-Liouville Fractional Order Partial Derivatives is Nonobjective. Preprints 2020, 2020080194 (doi: 10.20944/preprints202008.0194.v1). Balint, A.M.; Balint, S.; Birauas, S. Mathematical Description of Elastic Phenomena which Uses Caputo or Riemann-Liouville Fractional Order Partial Derivatives is Nonobjective. Preprints 2020, 2020080194 (doi: 10.20944/preprints202008.0194.v1).

Abstract

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

Subject Areas

objectivity of a mathematical description; elastic phenomena description; fractional order partial derivative

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