Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative

Abstract

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 $\psi =x+1$ 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 $\psi =x+1$ 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 $0.048640$ .