  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.
