Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative
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 fraction...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9006361 |
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| author | Muath Awadalla Yves Yannick Yameni Noupoue Kinda Abu Asbeh Noureddine Ghiloufi |
| author_facet | Muath Awadalla Yves Yannick Yameni Noupoue Kinda Abu Asbeh Noureddine Ghiloufi |
| author_sort | Muath Awadalla |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d8e1a15401a045f2ac0746b7014a6093 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d8e1a15401a045f2ac0746b7014a60932025-02-03T06:13:02ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9006361Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo DerivativeMuath Awadalla0Yves Yannick Yameni Noupoue1Kinda Abu Asbeh2Noureddine Ghiloufi3Department of Mathematics and StatisticsUniversité Catholique de LouvainDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsThis 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.http://dx.doi.org/10.1155/2022/9006361 |
| spellingShingle | Muath Awadalla Yves Yannick Yameni Noupoue Kinda Abu Asbeh Noureddine Ghiloufi Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative Journal of Mathematics |
| title | Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative |
| title_full | Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative |
| title_fullStr | Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative |
| title_full_unstemmed | Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative |
| title_short | Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative |
| title_sort | modeling drug concentration level in blood using fractional differential equation based on psi caputo derivative |
| url | http://dx.doi.org/10.1155/2022/9006361 |
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