On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense
Very recently, several novel conceptions of fractional derivatives have been proposed and employed to develop numerical simulations for a wide range of real-world configurations with memory, background, or non-local effects via an uncertainty parameter [0,1] as a confidence degree of belief. Under t...
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AIMS Press
2022-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022987?viewType=HTML |
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| author | Shao-Wen Yao Saima Rashid Mustafa Inc Ehab E. Elattar |
| author_facet | Shao-Wen Yao Saima Rashid Mustafa Inc Ehab E. Elattar |
| author_sort | Shao-Wen Yao |
| collection | DOAJ |
| description | Very recently, several novel conceptions of fractional derivatives have been proposed and employed to develop numerical simulations for a wide range of real-world configurations with memory, background, or non-local effects via an uncertainty parameter [0,1] as a confidence degree of belief. Under the complexities of the uncertainty parameter, the major goal of this paper is to develop and examine the Atangana-Baleanu derivative in the Caputo sense for a convoluted glucose-insulin regulating mechanism that possesses a memory and enables one to recall all foreknowledge. However, as compared to other existing derivatives, this is a vitally important point, and the convenience of employing this derivative lessens the intricacy of numerical findings. The Atangana-Baleanu derivative in the Caputo sense of fuzzy valued functions (FVF) in parameterized interval representation is established initially in this study. Then, it is leveraged to demonstrate that the existence and uniqueness of solutions were verified using the theorem suggesting the Banach fixed point and Lipschitz conditions under generalized Hukuhara differentiability. In order to explore the regulation of plasma glucose in diabetic patients with impulsive insulin injections and by monitoring the glucose level that returns to normal in a finite amount of time, we propose an impulsive differential equation model. It is a deterministic mathematical framework that is connected to diabetes mellitus and fractional derivatives. The framework for this research and simulations was numerically solved using a numerical approach based on the Adams-Bashforth-Moulton technique. The findings of this case study indicate that the fractional-order model's plasma glucose management is a suitable choice. |
| first_indexed | 2024-12-10T16:22:19Z |
| format | Article |
| id | doaj.art-0ccff88cf5764553bddc6857b4659428 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T16:22:19Z |
| publishDate | 2022-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0ccff88cf5764553bddc6857b46594282022-12-22T01:41:46ZengAIMS PressAIMS Mathematics2473-69882022-08-01710179131794110.3934/math.2022987On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy senseShao-Wen Yao0Saima Rashid1Mustafa Inc 2Ehab E. Elattar31. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China2. Department of Mathematics, Government College University, Faisalabad, Pakistan3. Department of Mathematics, Science Faculty, Firat University, Elazig 23119, Turkey 4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan5. Department of Electrical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif 21944, Saudi ArabiaVery recently, several novel conceptions of fractional derivatives have been proposed and employed to develop numerical simulations for a wide range of real-world configurations with memory, background, or non-local effects via an uncertainty parameter [0,1] as a confidence degree of belief. Under the complexities of the uncertainty parameter, the major goal of this paper is to develop and examine the Atangana-Baleanu derivative in the Caputo sense for a convoluted glucose-insulin regulating mechanism that possesses a memory and enables one to recall all foreknowledge. However, as compared to other existing derivatives, this is a vitally important point, and the convenience of employing this derivative lessens the intricacy of numerical findings. The Atangana-Baleanu derivative in the Caputo sense of fuzzy valued functions (FVF) in parameterized interval representation is established initially in this study. Then, it is leveraged to demonstrate that the existence and uniqueness of solutions were verified using the theorem suggesting the Banach fixed point and Lipschitz conditions under generalized Hukuhara differentiability. In order to explore the regulation of plasma glucose in diabetic patients with impulsive insulin injections and by monitoring the glucose level that returns to normal in a finite amount of time, we propose an impulsive differential equation model. It is a deterministic mathematical framework that is connected to diabetes mellitus and fractional derivatives. The framework for this research and simulations was numerically solved using a numerical approach based on the Adams-Bashforth-Moulton technique. The findings of this case study indicate that the fractional-order model's plasma glucose management is a suitable choice.https://www.aimspress.com/article/doi/10.3934/math.2022987?viewType=HTMLfractional diabetes modelatangana-baleanu fractional derivative operatorfuzzy set theorycontraction mapping theoremadams bashforth moulton method |
| spellingShingle | Shao-Wen Yao Saima Rashid Mustafa Inc Ehab E. Elattar On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense AIMS Mathematics fractional diabetes model atangana-baleanu fractional derivative operator fuzzy set theory contraction mapping theorem adams bashforth moulton method |
| title | On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense |
| title_full | On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense |
| title_fullStr | On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense |
| title_full_unstemmed | On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense |
| title_short | On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense |
| title_sort | on fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense |
| topic | fractional diabetes model atangana-baleanu fractional derivative operator fuzzy set theory contraction mapping theorem adams bashforth moulton method |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022987?viewType=HTML |
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