This work focuses on the problematic of modeling the drug diffusion process that occurs in the human body when an anesthetic drug is taken up. This is performed here using emerging tools from fractional calculus, i.e. by using fractional-order impedance models (FOIMs). A novel interpretation is given to the classical pharmacokinetic and pharmacodynamic models for drug uptake in the body. The major challenges that are encountered during this development consist of online identification of the patient model, introducing a logarithmic sampling time and embedding the proposed method in a closed loop control system.