TY - EJOU
AU - Awadalla, Muath
AU - Abuasbeh, Kinda
AU - Noupoue, Yves Yannick Yameni
AU - Abdo, Mohammed S.
TI - Modeling Drug Concentration in Blood through Caputo-Fabrizio and Caputo Fractional Derivatives
T2 - Computer Modeling in Engineering \& Sciences
PY - 2023
VL - 135
IS - 3
SN - 1526-1506
AB - This study focuses on the dynamics of drug concentration in the blood. In general, the concentration level of a drug
in the blood is evaluated by the mean of an ordinary and first-order differential equation. More precisely, it is solved
through an initial value problem. We proposed a new modeling technique for studying drug concentration in blood
dynamics. This technique is based on two fractional derivatives, namely, Caputo and Caputo-Fabrizio derivatives.
We first provided comprehensive and detailed proof of the existence of at least one solution to the problem; we
later proved the uniqueness of the existing solution. The proof was written using the Caputo-Fabrizio fractional
derivative and some fixed-point techniques. Stability via the Ulam-Hyers (UH) technique was also investigated. The
application of the proposed model on two real data sets revealed that the Caputo derivative was more suitable in this
study. Indeed, for the first data set, the model based on the Caputo derivative yielded a Mean Squared Error (MSE)
of 0.03095 with a corresponding best value of fractional order of derivative of 1.00360. Caputo-Fabrizio-basedderivative appeared to be the second-best method for the problem, with an MSE of 0.04324 for a corresponding best
fractional derivative order of 0.43532. For the second experiment, Caputo derivative-based model still performed
the best as it yielded an MSE of 0.04066, whereas the classical and the Caputo-Fabrizio methods were tied with
the same MSE of 0.07299. Another interesting finding was that the MSE yielded by the Caputo-Fabrizio fractional
derivative coincided with the MSE obtained from the classical approach.
KW - Pharmacokinetics; caputo fractional derivative; stability study; Caputo-Fabrizio fractional derivative
DO - 10.32604/cmes.2023.024036