Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation
Abstract In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population S ( t ) $\mathcal{S}(t)$ , the vaccinated population V ( t ) $\mathcal{V}(t)$ , the infected populati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01730-5 |
| _version_ | 1797840917918384128 |
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| author | Shiferaw Geremew Kebede Assia Guezane Lakoud |
| author_facet | Shiferaw Geremew Kebede Assia Guezane Lakoud |
| author_sort | Shiferaw Geremew Kebede |
| collection | DOAJ |
| description | Abstract In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population S ( t ) $\mathcal{S}(t)$ , the vaccinated population V ( t ) $\mathcal{V}(t)$ , the infected population I ( t ) $\mathcal{I}(t)$ , the recovered population R ( t ) $\mathcal{R}(t)$ , and the death class D ( t ) $\mathcal{D}(t)$ . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii’s fixed point theorem, Schauder’s fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem. |
| first_indexed | 2024-04-09T16:22:40Z |
| format | Article |
| id | doaj.art-47bfd93b21534537a0a48b325eb51c9a |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-09T16:22:40Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-47bfd93b21534537a0a48b325eb51c9a2023-04-23T11:24:00ZengSpringerOpenBoundary Value Problems1687-27702023-04-012023111710.1186/s13661-023-01730-5Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equationShiferaw Geremew Kebede0Assia Guezane Lakoud1Mathematics Department, College of Natural Science, Arba Minch UniversityMathematics Department, Faculty of Sciences, Badji Mokhtar Annaba UniversityAbstract In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population S ( t ) $\mathcal{S}(t)$ , the vaccinated population V ( t ) $\mathcal{V}(t)$ , the infected population I ( t ) $\mathcal{I}(t)$ , the recovered population R ( t ) $\mathcal{R}(t)$ , and the death class D ( t ) $\mathcal{D}(t)$ . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii’s fixed point theorem, Schauder’s fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem.https://doi.org/10.1186/s13661-023-01730-5Caputo–Fabrizio fractional derivativeFixed point theoremsExistenceUniquenessStability of solution |
| spellingShingle | Shiferaw Geremew Kebede Assia Guezane Lakoud Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation Boundary Value Problems Caputo–Fabrizio fractional derivative Fixed point theorems Existence Uniqueness Stability of solution |
| title | Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation |
| title_full | Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation |
| title_fullStr | Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation |
| title_full_unstemmed | Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation |
| title_short | Analysis of mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equation |
| title_sort | analysis of mathematical model involving nonlinear systems of caputo fabrizio fractional differential equation |
| topic | Caputo–Fabrizio fractional derivative Fixed point theorems Existence Uniqueness Stability of solution |
| url | https://doi.org/10.1186/s13661-023-01730-5 |
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