This article studies a pharmacokinetics problem, which is the mathematical modeling of a drug concentration variation in human blood, starting from the injection time. Theories and applications of fractional calculus are the main tools through which we establish main results. The psi-Caputo fractional derivative plays a substantial role in the study. We prove the existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The application of the theoretical results on two data sets shows the following results. For the first data set, a psi-Caputo with the kernel
ψ
=
x
+
1
is the best approach as it yields a mean square error (MSE) of
0.04065
. The second best is the simple fractional method whose MSE is
0.05814
; finally, the classical approach is in the third position with an MSE of
0.07299
. For the second data set, a psi-Caputo with the kernel
ψ
=
x
+
1
is the best approach as it yields an MSE of
0.03482
. The second best is the simple fractional method whose MSE is
0.04116
and, finally, the classical approach with an MSE of
0.048640
.