On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory
A novel two-compartment model for drug release was formulated. The general fractional derivatives of a specific type and distributed order were used in the formulation. Earlier used models in pharmacokinetics with fractional derivatives follow as special cases of the model proposed here. As a first...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/7/518 |
| _version_ | 1797589226401824768 |
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| author | Vesna Miskovic-Stankovic Teodor M. Atanackovic |
| author_facet | Vesna Miskovic-Stankovic Teodor M. Atanackovic |
| author_sort | Vesna Miskovic-Stankovic |
| collection | DOAJ |
| description | A novel two-compartment model for drug release was formulated. The general fractional derivatives of a specific type and distributed order were used in the formulation. Earlier used models in pharmacokinetics with fractional derivatives follow as special cases of the model proposed here. As a first application, we used this model to study the release of gentamicin from poly(vinyl alcohol)/chitosan/gentamicin (PVA/CHI/Gent) hydrogel aimed at wound dressing in the medical treatment of deep chronic wounds. As a second application, we studied the release of gentamicin from antibacterial biodynamic hydroxyapatite/poly(vinyl alcohol) /chitosan/gentamicin (HAP/PVA/CS/Gent) coating on a titanium substrate for bone tissue implants, which enables drug delivery directly to the infection site. In both cases. a good agreement is obtained between the measured data and the data calculated from the model proposed here. The form of the general fractional derivatives used here results in an additional parameter in the compartmental model used here. This, as a consequence, leads to a better approximation of the experimental data with only a slightly more complicated numerical procedure in obtaining the solution. |
| first_indexed | 2024-03-11T01:03:30Z |
| format | Article |
| id | doaj.art-3a7a26b7a4a54801a52114066d53d724 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T01:03:30Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-3a7a26b7a4a54801a52114066d53d7242023-11-18T19:25:51ZengMDPI AGFractal and Fractional2504-31102023-06-017751810.3390/fractalfract7070518On a System of Equations with General Fractional Derivatives Arising in Diffusion TheoryVesna Miskovic-Stankovic0Teodor M. Atanackovic1Faculty of Ecology and Environmental Protection, University Union-Nikola Tesla, 11000 Belgrade, SerbiaFaculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, SerbiaA novel two-compartment model for drug release was formulated. The general fractional derivatives of a specific type and distributed order were used in the formulation. Earlier used models in pharmacokinetics with fractional derivatives follow as special cases of the model proposed here. As a first application, we used this model to study the release of gentamicin from poly(vinyl alcohol)/chitosan/gentamicin (PVA/CHI/Gent) hydrogel aimed at wound dressing in the medical treatment of deep chronic wounds. As a second application, we studied the release of gentamicin from antibacterial biodynamic hydroxyapatite/poly(vinyl alcohol) /chitosan/gentamicin (HAP/PVA/CS/Gent) coating on a titanium substrate for bone tissue implants, which enables drug delivery directly to the infection site. In both cases. a good agreement is obtained between the measured data and the data calculated from the model proposed here. The form of the general fractional derivatives used here results in an additional parameter in the compartmental model used here. This, as a consequence, leads to a better approximation of the experimental data with only a slightly more complicated numerical procedure in obtaining the solution.https://www.mdpi.com/2504-3110/7/7/518general fractional derivative of distributed ordergentamicin release |
| spellingShingle | Vesna Miskovic-Stankovic Teodor M. Atanackovic On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory Fractal and Fractional general fractional derivative of distributed order gentamicin release |
| title | On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory |
| title_full | On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory |
| title_fullStr | On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory |
| title_full_unstemmed | On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory |
| title_short | On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory |
| title_sort | on a system of equations with general fractional derivatives arising in diffusion theory |
| topic | general fractional derivative of distributed order gentamicin release |
| url | https://www.mdpi.com/2504-3110/7/7/518 |
| work_keys_str_mv | AT vesnamiskovicstankovic onasystemofequationswithgeneralfractionalderivativesarisingindiffusiontheory AT teodormatanackovic onasystemofequationswithgeneralfractionalderivativesarisingindiffusiontheory |