Time domain response for the fractional order transfer function characterizing the thermal diffusive interface

The time response is one of the main concerns when controlling and analyzing a system. Getting this response for some systems is sometimes difficult especially if the transfer function modelling this system is non-integer or nonlinear. The thermal diffusive interface is an example of such systems. In fact, when considering the semi-infinite homogeneous plane, the time response can be analytically calculated for some particular input functions as the step or the impulse but can´t be determined for any type of inputs. As for the finite homogeneous plane, the time response can´t be found analytically for any input. Hence, this paper presents some novel methods to approach this system and to get the time response with some light approximations on the exact system. The results show that the approximation made in the frequency domain have almost the same behavior of the exact transfer function and the time domain response could be computed, using this approximation, for any input for both thermal systems.