On the consistency of local fractional semilinear Duhem model

In this paper, we introduce the local fractional semilinear and the local fractional Dahl models and investigate their consistency with hysteresis. The notion of consistency was initially introduced in Ikhouane (Math Control Signals Syst 25:294–310) to analyze the hysteretic behavior of causal systems and to describe analytically the so-called “hysteresis loops”. The validity of our results is confirmed by numerical simulations.