  We present a novel Pharmacokinetic/Pharmacodynamic (PK/PD) model for the
induction phase of anesthesia, incorporating the $\psi$-Caputo fractional
derivative. By employing the Picard iterative process, we derive a solution for
a nonhomogeneous $\psi$-Caputo fractional system to characterize the dynamical
behavior of the drugs distribution within a patient's body during the
anesthesia process. To explore the dynamics of the fractional anesthesia model,
we perform numerical analysis on solutions involving various functions of
$\psi$ and fractional orders. All numerical simulations are conducted using the
MATLAB computing environment. Our results suggest that the $\psi$ functions and
the fractional order of differentiation have an important role in the modeling
of individual-specific characteristics, taking into account the complex
interplay between drug concentration and its effect on the human body. This
innovative model serves to advance the understanding of personalized drug
responses during anesthesia, paving the way for more precise and tailored
approaches to anesthetic drug administration.
