Modelling and simulations in time-fractional electrodynamics based on control engineering methods

In this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell's equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. In particular, we derive continuous-time analytical solutions based on state-transition matrices for electromagnetic-wave propagation in the TF media. Then, discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. It is demonstrated that the proposed models give the same results as other reference methods presented in the literature. However, due to the application of finite-difference scheme, they remain more flexible in terms of the number of simulation scenarios which can be tackled.