In classical mechanics objectivity lost when Riemann-Liouwille or Caputo fractional order derivatives are used

TL;DR

This paper argues that using Riemann-Liouville or Caputo fractional derivatives in classical mechanics compromises the objectivity of physical descriptions, raising questions about the interpretation of such models.

Contribution

It highlights the loss of objectivity in mechanical descriptions when fractional derivatives are used, questioning their validity in physical modeling.

Findings

Fractional derivatives can lead to non-objective descriptions of mechanical systems.

Recent literature often neglects the issue of objectivity in fractional models.

The paper questions the interpretation of results from non-objective models.

Abstract

In section.1 the objectivity in science is presented shortly. In section.2 some details concerning the objectivity in the case of the mechanical movement description of a material particle are given. In section.3 details concerning the objectivity of the description in the Newtonian continuum mechanics are given. The Riemann-Liouville and the Caputo fractional order derivatives are presented shortly in section 4. In section 5 the lost of the objectivity of the mechanical movement descriptions, presented in sections 2,3, due to the use of the Riemann-Liouville or the Caputo fractional order derivatives is presented. This is followed, in section 6, by the presentation of some recent papers which propose the use of these fractional order derivatives, instead of the integer order derivatives, in the description of some physical phenomena. It is underlined that the objectivity in these last papers is ignored. At the end of the present paper instead of conclusion we formulate the following question: if a mathematical description of a real phenomenon is not objective then what is the interpretation of the reported results and how this results have to be used?