This article studies a pharmacokinetics problem which is the mathematical modeling of a drug concentration in a human blood over time, starting from when the drug is administered. Results are obtained using fractional calculus theories. A fractional derivative known as Psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. Application of the results on a data set showed that a psi-Caputo with the kernel ψ = x + 1 was the best approach as it leaded to mean square error of 0.04065. The second best was the simple fractional method whose error was 0.05814 and, finally the classical approach with an error of 0.07299.