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This paper presents three fractional models formulated from a classicalPharmacokinetics compartmental system: commensurable, non-commensurable, andimplicit non-commensurable models. Their distinguishing characteristics arefurther examined comprehensively. Because analytic solutions for such modelsare typically challenging to obtain, we study the application of the FractionalFinite Difference Method (FFDM) to simulate approximate solutions. Thecharacteristic of the non-commensurable model is shown to be incompatible withthe concept of mass balance. However, it appeared to outlast fractionalcalculus theory when simulating anomalous kinetics. We proved this by fittingthe proposed fractional and classical models to an experimental data set(amiodarone) and estimated the parameters using the least-square approach. Theclassical model diverged, but the non-commensurable model predicted a fitcomparable to the other two fractional models. The fractional models describedanomalous diffusion better than classical theories. The numerical resultsshowed that the proposed numerical method is equally efficient in solving anycomplex compartmental models, as they performed well in simulations for theclassic example of the model.

Investigation of Fractional Compartmental Models with Application to Amiodarone Drug Diffusion in Pharmacokinetics