Mathematical description of the bulk fluid flow and that of the contained impurity dispersion which uses Caputo or Riemann-Liouville fractional order partial derivatives is nonobjective

Abstract

In this paper it is shown that the mathematical description of a Newtonian, incompressible, viscous bulk fluid flow and that of the contained impurity dispersion which uses Caputo or Riemann-Liouville fractional order derivative, having integral representation on finite interval, is nonobjective. This means that, two different observers describing the flow or the contained impurity dispersion with these tools obtain two different results which cannot be reconciled i.e. transformed into each other using only formulas that link the coordinates of a point in two fixed orthogonal reference frames and formulas that link the numbers representing a 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 of the obtained results is correct?

Keywords

• objectivity of a mathematical description
• bulk fluid flow
• impurity dispersion
• fractional order partial derivative