ADVANCED FRACTIONAL MODELING OF PHARMACOKINETIC PROCESSES USING mABC AND HILFER DERIVATIVES

This paper investigates the pharmacokinetic journey of medicines in the human body specifically the stages of absorption, distribution, biochemical transformation, and elimination — through advanced mathematical modeling. To more accurately capture the complex dynamics of drug behavior, three distinct models are developed using nonlocal fractional derivatives, namely the modified Atangana–Baleanu–Caputo (mABC) and Hilfer operators. These fractional frameworks extend beyond classical approaches, enabling a more realistic representation of memory effects and anomalous diffusion in biological systems. Each model is tailored to the unique properties of the fractional operators employed, allowing a detailed examination of diffusion processes and concentration dynamics. The Laplace transform method is applied as an effective analytical tool to handle the complexities of the fractional differential equations and to predict the time-dependent evolution of drug concentrations across compartments. This modeling approach offers valuable insights into pharmacokinetics by enhancing the precision of dosage prediction and optimizing therapeutic outcomes. The integration of nonlocal fractional operators provides a powerful framework for understanding drug behavior at the biochemical level, contributing meaningfully to ongoing research in pharmacology, biochemistry, and systems biology.