This study proposes compartment models with the Caputo fractional derivative to capture drug dynamics across absorption, central, and peripheral compartments, and to account for memory effects and anomalous kinetics. The first part of the study covers mathematical modeling, which enables analysis of the amount of drug in each compartment using closed-form expressions. The second part is to estimate the pharmacokinetic parameters and compare models using the Akaike information criterion and Bayesian information criterion for the drugs pindolol, fenoprofen, and cyclosporin A. The regression analysis was performed by using the corresponding Mittag-Leffler regression model and the trust-region algorithm with the Adams predictor-corrector method.