Comparative study of blood sugar–insulin model using fractional derivatives

Abstract

ABSTRACTMany years have passed since the model that outlined the connection between sugar and insulin was developed, and a great deal of study and investigation has subsequently been done on it. In this work, we investigated the disparities in the Modified Bergman's glucose–insulin model between Yang–Abdel–Cattani derivative and Caputo–Fabrizio derivative. With our improvements, the prior model now includes the diet, which is a crucial component of the blood glucose model. Based on results, the new model outperforms the previous one in terms of accuracy. To highlight the significance of fractional derivatives, we also established the fractional models. In addition, we verified the existence and uniqueness of the results and offered a graphical and numerical depiction of the findings.

Keywords

• Bergman's minimal model
• Caputo–Fabrizio derivative
• Yang–Abdel–Cattani derivative
• Sumudu transform
• uniqueness and oneness
• Primary 92B05