# For guitar string, the mathematical description of strain, constitutive law, and dynamics, by direct replacement of integer order derivatives with classic Caputo or Riemann-Liouville fractional order partial derivatives is nonobjective

### Abstract

In this paper it is proven that, in case of a guitar string, the mathematical description of strain, obtained by direct replacement of integer order spatial derivatives with classic Caputo or Riemann-Liouville fractional order spatial partial derivatives, is nonobjective. It is also proven that ,in case of a guitar string, the mathematical description of the stress-strain relation (constitutive law),obtained by applying to the right hand side of Hooke relation the classic Caputo or Riemann-Liouville fractional order temporal partial derivative, is nonobjective. Finally it is proven that, in case of a guitar string, the mathematical description of dynamics, obtained by direct replacement of integer order temporal partial derivative with classic Caputo or Riemann-Liouville fractional order temporal partial derivative, 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.