A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods
The regulation of blood glucose levels involves complex interactions between glucose, insulin, and beta cells, where disruptions may lead to diabetes. Traditional integer-order models fail to capture the memory-dependent and hereditary properties of biological systems. This study develops a fraction...
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| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2025.2460280 |
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| author | Khalid I. A. Ahmed Safa M. Mirgani Aly Seadawy Sayed Saber |
| author_facet | Khalid I. A. Ahmed Safa M. Mirgani Aly Seadawy Sayed Saber |
| author_sort | Khalid I. A. Ahmed |
| collection | DOAJ |
| description | The regulation of blood glucose levels involves complex interactions between glucose, insulin, and beta cells, where disruptions may lead to diabetes. Traditional integer-order models fail to capture the memory-dependent and hereditary properties of biological systems. This study develops a fractional-order glucose-insulin-beta cell model and investigates its dynamics using the Residual Power Series Method (RPSM) and the Generalized Runge-Kutta Method (GRKM). Theoretical analyses establish the model's existence, uniqueness, and boundedness of solutions, ensuring biological validity. Stability and bifurcation analyses reveal the critical role of fractional orders in shaping system dynamics. RPSM demonstrates computational efficiency with rapid convergence, while GRKM excels in stability and bifurcation studies. Comparative numerical simulations highlight the complementary strengths of these methods, providing a robust framework for predictive modeling in diabetes management. This work underscores the potential of fractional-order models to advance understanding and control of metabolic disorders. |
| format | Article |
| id | doaj-art-cfb641ffb6d64ac5a87796c4d6b0389c |
| institution | Kabale University |
| issn | 1658-3655 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj-art-cfb641ffb6d64ac5a87796c4d6b0389c2025-02-03T13:56:19ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552025-12-0119110.1080/16583655.2025.2460280A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methodsKhalid I. A. Ahmed0Safa M. Mirgani1Aly Seadawy2Sayed Saber3Department of Basic Sciences, Deanship of the Preparatory Year, Najran University, Najran, Saudi ArabiaImam Mohammed Ibn Saud Islamic University (IMSIU), College of Science Department of Mathematics and Statistics, Riyadh, Saudi ArabiaMathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Kingdom of Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi ArabiaThe regulation of blood glucose levels involves complex interactions between glucose, insulin, and beta cells, where disruptions may lead to diabetes. Traditional integer-order models fail to capture the memory-dependent and hereditary properties of biological systems. This study develops a fractional-order glucose-insulin-beta cell model and investigates its dynamics using the Residual Power Series Method (RPSM) and the Generalized Runge-Kutta Method (GRKM). Theoretical analyses establish the model's existence, uniqueness, and boundedness of solutions, ensuring biological validity. Stability and bifurcation analyses reveal the critical role of fractional orders in shaping system dynamics. RPSM demonstrates computational efficiency with rapid convergence, while GRKM excels in stability and bifurcation studies. Comparative numerical simulations highlight the complementary strengths of these methods, providing a robust framework for predictive modeling in diabetes management. This work underscores the potential of fractional-order models to advance understanding and control of metabolic disorders.https://www.tandfonline.com/doi/10.1080/16583655.2025.2460280Fractional calculusglucose-insulin dynamicsresidual power series methodgeneralized Runge-Kutta methodstability analysisdiabetes modeling |
| spellingShingle | Khalid I. A. Ahmed Safa M. Mirgani Aly Seadawy Sayed Saber A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods Journal of Taibah University for Science Fractional calculus glucose-insulin dynamics residual power series method generalized Runge-Kutta method stability analysis diabetes modeling |
| title | A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods |
| title_full | A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods |
| title_fullStr | A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods |
| title_full_unstemmed | A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods |
| title_short | A comprehensive investigation of fractional glucose-insulin dynamics: existence, stability, and numerical comparisons using residual power series and generalized Runge-Kutta methods |
| title_sort | comprehensive investigation of fractional glucose insulin dynamics existence stability and numerical comparisons using residual power series and generalized runge kutta methods |
| topic | Fractional calculus glucose-insulin dynamics residual power series method generalized Runge-Kutta method stability analysis diabetes modeling |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2025.2460280 |
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