# Fractional Calculus in Pharmacokinetics

## TL;DR

This paper introduces fractional pharmacokinetics, a new approach using non-integer differential equations to model drug dynamics, highlighting its clinical significance and discussing numerical and control methods for personalized treatment design.

## Contribution

It presents the foundational theory of fractional pharmacokinetics, reviews existing applications, and explores numerical simulation and optimal control techniques for drug dosing.

## Key findings

- Fractional models better capture irregular drug accumulation patterns.
- Numerical methods enable accurate simulation of fractional pharmacokinetics.
- Optimal control strategies can personalize drug dosing protocols.

## Abstract

We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.