Ahmad, AqeelFarman, MuhammadAkgül, Ali2024-12-242024-12-2420202587-2648https://doi.org10.31197/atnaa.778506https://hdl.handle.net/20.500.12604/4058In this article, we research the diabetes model and its consequences using the Caputo and Atangana Baleanu fractional derivatives. A deterministic mathematical model is corresponding to the fractional derivative of diabetes mellitus. The Laplace transformation is used for the diagnostic structure of the diabetes model. Picard-Lindelof 's method shows the existence and uniqueness of the solution. Finally, numerical simulations are made to illustrate the effects of changing the fractional-order to obtain the theoretical results, and comparisons are made for the Caputo and Atangana Baleanu derivative. The results of the following work by controlling plasma glucose with the fractional-order model make it a suitable candidate for controlling human type 1 diabetes. © 2020, Erdal Karapinar. All rights reserved.eninfo:eu-repo/semantics/openAccessABC derivativeFixed point theoremFractional order glucose insulin systemPicardas lindelof approachStabilityArticle44483497Q12-s2.0-8509931583810.31197/atnaa.778506