Mathematical description of the bulk gas flow and that of the content impurity dispersion, which use temporal Caputo or Riemann-Liouville fractional order partial derivatives is nonobjective

Abstract

In this paper, it is shown that the mathematical description of the flow of an inviscid, compressible, non-heat conducting, isentropic, perfect bulk gas, and that of the contained impurity dispersion, which uses temporal Caputo or Riemann-Liouville fractional order derivative having integral representation on a finite interval, is nonobjective. The basic idea is that this type of description is not invariant when the orthogonal reference frame or the origin of time measuring change. Due to that, two observers describing the same flow or impurity dispersion with these mathematical tools obtain different results which cannot be reconciled (translated into each other) using transformations which relate the coordinate of the same point in two fixed orthogonal reference frame and transformations which relate the numbers which represent the same moment of time in two different choice 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?