Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions

The aim of this paper is to provide a mathematical study of the amount of drug administered as a continuous intravenous infusion or oral dose. For this purpose, we consider fractional-order mammillary-type models describing the anomalous dynamics of exchange of concentrations between compartments at, constant input rates, power-law type, and in the form of oral doses at given (discrete) times. We have developed a general analysis strategy for these models, in which we have found closed-form analytical solutions written in terms of the multivariate Mittag-Leffler function. Numerical simulations have been performed using our formulas, with parameters from the literature.