Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative. (28th September 2022) - Awadalla, Muath; Noupoue, Yves Yannick Yameni; Asbeh, Kinda Abu; Ghiloufi, Noureddine
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 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 .