In this paper, a novel fractional-order element (FOE) is modeled in a wide frequency range. The FOE is based on a green biopolymer, i.e., bacterial cellulose (BC), infused with ionic liquids (ILs). The modeling is performed in the frequency domain and a lumped-circuit model is proposed. The model is an evolution with respect to a simpler one already introduced by the authors, for a narrower frequency range. Results show that ILs generate a quite complex frequency domain behavior, which can be described in the framework of FOEs. Furthermore, results on the time stability of the device under investigation are given.