Approximation and identification of diffusive interfaces by fractional models

Heat transfer problems obey to diffusion phenomenon. In this paper we show that they can be modelled with the help of fractional systems. The simulation is based on a fractional integrator operator where the non-integer behaviour acts only over a limited spectral band. Starting with frequency considerations derived from the analysis of a diffusion problem, a more general approximation of the fractional system is proposed. A state-space model is presented that gives an accurate simulation for transients, and with which it is possible to carry out an output-error technique to estimate the model parameters. Numerical simulations of the heat transfer problem are used to illustrate the improvements of the proposed model.