Approximation of a thermal diffusive interface fractional-order system — Part 1: Application to a semi-infinite plane

The fractional differentiation and integration exist in natural phenomena or can be artificially introduced into other domains. Concerning the thermal diffusive interface, the fractional expression is emphasized when taking the applied flux as input for the system and the measured temperature at any point as an output. However, the main problem when facing such systems is to pass from the frequency domain to the time domain in order to estimate the response of the system at any point for any input at any instance. So, the aim of this work is to present a method to approximate the fractional system that models the semi-infinite plane medium. The second part of this work presents the approximation of a finite plane medium. The results show that the approximation leads to very good behaviour.