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A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors
The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9975863/ https://www.ncbi.nlm.nih.gov/pubmed/37360279 http://dx.doi.org/10.1007/s40435-023-01131-7 |
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author | Karaagac, Berat Owolabi, Kolade M. Pindza, Edson |
author_facet | Karaagac, Berat Owolabi, Kolade M. Pindza, Edson |
author_sort | Karaagac, Berat |
collection | PubMed |
description | The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard’s theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions [Formula: see text] and [Formula: see text] leads to an increase in the number of people living with diabetes mellitus. |
format | Online Article Text |
id | pubmed-9975863 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-99758632023-03-01 A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors Karaagac, Berat Owolabi, Kolade M. Pindza, Edson Int J Dyn Control Article The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard’s theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions [Formula: see text] and [Formula: see text] leads to an increase in the number of people living with diabetes mellitus. Springer Berlin Heidelberg 2023-03-01 /pmc/articles/PMC9975863/ /pubmed/37360279 http://dx.doi.org/10.1007/s40435-023-01131-7 Text en © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Karaagac, Berat Owolabi, Kolade M. Pindza, Edson A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors |
title | A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors |
title_full | A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors |
title_fullStr | A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors |
title_full_unstemmed | A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors |
title_short | A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors |
title_sort | computational technique for the caputo fractal-fractional diabetes mellitus model without genetic factors |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9975863/ https://www.ncbi.nlm.nih.gov/pubmed/37360279 http://dx.doi.org/10.1007/s40435-023-01131-7 |
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