ON THE FRACTIONAL MODELLING OF THE DIFFUSIVE INTERFACE

This paper deals with the fractional order modelling of a heat transfer diffusive interface, which is considered as a prototype problem. Based on the truncation of the diffusive interface model, we demonstrate that commensurate fractional order models, where the basic order is n=0.5, are natural candidates for the approximation of the diffusive model. Then, we show that frequency approximation can be improved by optimization of the models parameters, using a least squares technique. Non commensurate fractional order models can be also considered as an excellent alternative to the approximation of the diffusive interface, with less model complexity. The main conclusion of this paper is that a diffusive interface can be approximated by two families of fractional models with appropriate and necessary complexity.