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. Preprints2020, 2020080194. https://doi.org/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. https://doi.org/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. Preprints2020, 2020080194. https://doi.org/10.20944/preprints202008.0194.v1
APA Style
Balint, A. M., Balint, S., & Birauas, S. (2020). Mathematical Description of Elastic Phenomena which Uses Caputo or Riemann-Liouville Fractional Order Partial Derivatives is Nonobjective. Preprints. https://doi.org/10.20944/preprints202008.0194.v1
Chicago/Turabian Style
Balint, A. M., Stefan Balint and Silviu Birauas. 2020 "Mathematical Description of Elastic Phenomena which Uses Caputo or Riemann-Liouville Fractional Order Partial Derivatives is Nonobjective" Preprints. https://doi.org/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?
Keywords
objectivity of a mathematical description; elastic phenomena description; fractional order partial derivative
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.