A Fractional Epidemiological Model for Bone Remodeling Process
This article focuses on modeling bone formation process using a fractional differential approach, named bones remodeling process. The first goal of the work is to investigate existence and uniqueness of the proposed fractional differential model. The next goal is to investigate how similar is the pr...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1614774 |
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| author | Muath Awadalla Yves Yannick Yameni Noupoue Kinda Abuasbeh |
| author_facet | Muath Awadalla Yves Yannick Yameni Noupoue Kinda Abuasbeh |
| author_sort | Muath Awadalla |
| collection | DOAJ |
| description | This article focuses on modeling bone formation process using a fractional differential approach, named bones remodeling process. The first goal of the work is to investigate existence and uniqueness of the proposed fractional differential model. The next goal is to investigate how similar is the proposed approach to the method based on system classical differential equations. The dynamical system of equations used is built upon three main parameters. These are chemical substances, namely, calcitonin secretion, osteoclastic and osteoblastic, which are involved in the bone’s formation process. We implement some numerical simulations to graphically show the impact of an arbitrary fractional order of derivative. We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. Flexibility in the choice of the fractional order of derivative is an advantage as it helps in selecting the best fractional order of derivative. |
| format | Article |
| id | doaj-art-8e3b1719b6ab46af9ac26aed6b3f238a |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8e3b1719b6ab46af9ac26aed6b3f238a2025-02-03T01:01:06ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/1614774A Fractional Epidemiological Model for Bone Remodeling ProcessMuath Awadalla0Yves Yannick Yameni Noupoue1Kinda Abuasbeh2Department of Mathematics and StatisticsInstitute of Statistics, Biostatistics and Actuarial Sciences (ISBA)Department of Mathematics and StatisticsThis article focuses on modeling bone formation process using a fractional differential approach, named bones remodeling process. The first goal of the work is to investigate existence and uniqueness of the proposed fractional differential model. The next goal is to investigate how similar is the proposed approach to the method based on system classical differential equations. The dynamical system of equations used is built upon three main parameters. These are chemical substances, namely, calcitonin secretion, osteoclastic and osteoblastic, which are involved in the bone’s formation process. We implement some numerical simulations to graphically show the impact of an arbitrary fractional order of derivative. We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. Flexibility in the choice of the fractional order of derivative is an advantage as it helps in selecting the best fractional order of derivative.http://dx.doi.org/10.1155/2021/1614774 |
| spellingShingle | Muath Awadalla Yves Yannick Yameni Noupoue Kinda Abuasbeh A Fractional Epidemiological Model for Bone Remodeling Process Journal of Mathematics |
| title | A Fractional Epidemiological Model for Bone Remodeling Process |
| title_full | A Fractional Epidemiological Model for Bone Remodeling Process |
| title_fullStr | A Fractional Epidemiological Model for Bone Remodeling Process |
| title_full_unstemmed | A Fractional Epidemiological Model for Bone Remodeling Process |
| title_short | A Fractional Epidemiological Model for Bone Remodeling Process |
| title_sort | fractional epidemiological model for bone remodeling process |
| url | http://dx.doi.org/10.1155/2021/1614774 |
| work_keys_str_mv | AT muathawadalla afractionalepidemiologicalmodelforboneremodelingprocess AT yvesyannickyameninoupoue afractionalepidemiologicalmodelforboneremodelingprocess AT kindaabuasbeh afractionalepidemiologicalmodelforboneremodelingprocess AT muathawadalla fractionalepidemiologicalmodelforboneremodelingprocess AT yvesyannickyameninoupoue fractionalepidemiologicalmodelforboneremodelingprocess AT kindaabuasbeh fractionalepidemiologicalmodelforboneremodelingprocess |