Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model
The initial value problem in Cauchy-type under the $ (k, \psi) $-Caputo proportional fractional operators was our focus in this paper. An extended Gronwall inequality and its properties were analyzed. The existence and uniqueness results were proven utilizing the fixed point theory of Banach's...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241622 |
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| author | Weerawat Sudsutad Chatthai Thaiprayoon Aphirak Aphithana Jutarat Kongson Weerapan Sae-dan |
| author_facet | Weerawat Sudsutad Chatthai Thaiprayoon Aphirak Aphithana Jutarat Kongson Weerapan Sae-dan |
| author_sort | Weerawat Sudsutad |
| collection | DOAJ |
| description | The initial value problem in Cauchy-type under the $ (k, \psi) $-Caputo proportional fractional operators was our focus in this paper. An extended Gronwall inequality and its properties were analyzed. The existence and uniqueness results were proven utilizing the fixed point theory of Banach's and Leray-Schauder's types. The qualitative analysis included results for Ulam-Mittag-Leffler stability, which was also investigated. Using a decomposition principle, a novel numerical technique was presented for the $ (k, \psi) $-Caputo proportional fractional derivative operator. Finally, theoretical results were supported with numerical examples to demonstrate their practical application, especially to blood alcohol level problems. |
| format | Article |
| id | doaj-art-cac51c2e98eb421fa74c4a438fd5a0d5 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-cac51c2e98eb421fa74c4a438fd5a0d52025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912340133404110.3934/math.20241622Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels modelWeerawat Sudsutad0Chatthai Thaiprayoon1Aphirak Aphithana2Jutarat Kongson3Weerapan Sae-dan4Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, ThailandResearch Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, ThailandDepartment of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, ThailandResearch Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, ThailandDepartment of Computer Engineering, Faculty of Engineering, Ramkhamkaeng University, Bangkok 10240, ThailandThe initial value problem in Cauchy-type under the $ (k, \psi) $-Caputo proportional fractional operators was our focus in this paper. An extended Gronwall inequality and its properties were analyzed. The existence and uniqueness results were proven utilizing the fixed point theory of Banach's and Leray-Schauder's types. The qualitative analysis included results for Ulam-Mittag-Leffler stability, which was also investigated. Using a decomposition principle, a novel numerical technique was presented for the $ (k, \psi) $-Caputo proportional fractional derivative operator. Finally, theoretical results were supported with numerical examples to demonstrate their practical application, especially to blood alcohol level problems.https://www.aimspress.com/article/doi/10.3934/math.20241622gronwall inequalityexistence and uniquenessblood alcohol dynamic model$ (k, \psi) $-caputo proportional fractional derivativeulam-mittag-leffler stability |
| spellingShingle | Weerawat Sudsutad Chatthai Thaiprayoon Aphirak Aphithana Jutarat Kongson Weerapan Sae-dan Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model AIMS Mathematics gronwall inequality existence and uniqueness blood alcohol dynamic model $ (k, \psi) $-caputo proportional fractional derivative ulam-mittag-leffler stability |
| title | Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model |
| title_full | Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model |
| title_fullStr | Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model |
| title_full_unstemmed | Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model |
| title_short | Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model |
| title_sort | qualitative results and numerical approximations of the k psi caputo proportional fractional differential equations and applications to blood alcohol levels model |
| topic | gronwall inequality existence and uniqueness blood alcohol dynamic model $ (k, \psi) $-caputo proportional fractional derivative ulam-mittag-leffler stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241622 |
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