Objectivity Lost when Riemann-Liouville or Caputo Fractional Order Derivatives Are Used

(joint work with Agneta Balint)

Abstract. In this paper the objectivity in science, the Riemann-Liouville and the Caputo fractional order derivatives are presented shortly. This is followed 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. The objectivity of the new mathematical concepts, constitutive equations, evolution equations in these papers is not considered. In the present paper it is shown that in classical mechanics when Riemann-Liouville or Caputo fractional derivatives are used, the objectivity of the new concepts, constitutive relations, evolution equations, is lost. With this aim this study was undertaken.