  This paper presents three fractional models formulated from a classical
Pharmacokinetics compartmental system: commensurable, non-commensurable, and
implicit non-commensurable models. Their distinguishing characteristics are
further examined comprehensively. Because analytic solutions for such models
are typically challenging to obtain, we study the application of the Fractional
Finite Difference Method (FFDM) to simulate approximate solutions. The
characteristic of the non-commensurable model is shown to be incompatible with
the concept of mass balance. However, it appeared to outlast fractional
calculus theory when simulating anomalous kinetics. We proved this by fitting
the proposed fractional and classical models to an experimental data set
(amiodarone) and estimated the parameters using the least-square approach. The
classical model diverged, but the non-commensurable model predicted a fit
comparable to the other two fractional models. The fractional models described
anomalous diffusion better than classical theories. The numerical results
showed that the proposed numerical method is equally efficient in solving any
complex compartmental models, as they performed well in simulations for the
classic example of the model.
