A control of glucose level in insulin therapies for the development of artificial pancreas by Atangana Baleanu derivative q Muhammad Farman a, * , Muhammad Umer Saleem b , Aqeel Ahmad a , Sumaiyah Imtiaz a , Muhammad Farhan Tabassum c , Sana Akram d , M.O. Ahmad a a Department of Mathematics and Statistics, University of Lahore, Lahore 54590, Pakistan b Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan c Department of Sports Sciences, Faculty of Allied Health Science, University of Lahore, Lahore, Pakistan d Department of Mathematics, Lahore Garrison University, Lahore, Pakistan Received 2 December 2019; revised 19 April 2020; accepted 26 April 2020 KEYWORDS Fractional order glucose insulin; Artificial pancreas; Stability; Insulin therapy; ABC derivative Abstract In this paper, we analyze the fractional modeling of diabetes mellitus model using the definitions of Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, The primary aim of this article is to create and evaluate a fractional order derivatives system for an extensive regulatory scheme of glucose insulin regulation for glucose insulin pump to control diabetes. The existence and uniqueness are determined by fixed point theorem and an iterative scheme. We sug- gest an impulsive differential equation model to study plasma glucose control for diabetic patients with impulsive insulin injections and by measuring the glucose level which leads to normal level in finite time. It is regarded as deterministic fractional derivative model related to the diabetes mellitus which provide the better control strategy at fractional values for the development of artificial pan- creas. For different fractional orders, numerical simulations are performed to demonstrate the impacts of varying the fractional order to achieve the theoretical outcomes and comparison is made for the caputo and caputo fabrizio derivative. The results of these case studies by controlling plasma glucose with fractional order model makes it an appropriate candidate to control the type 1 diabetes in human. Ó 2020 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction Pancreas produces insulin and glucagon hormones that help in regulation of blood sugar levels. Insulin is secreted through pancreas into the blood when blood glucose level is high. If blood glucose is low,glycogen is produced through breakage * Corresponding author. E-mail address: muhammad.farman@math.uol.edu.pk (M. Farman). q Peer review under responsibility of Faculty of Engineering, Alexandria University. Alexandria Engineering Journal (2020) xxx, xxx–xxx HOSTED BY Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com https://doi.org/10.1016/j.aej.2020.04.027 1110-0168 Ó 2020 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M. Farman et al., A control of glucose level in insulin therapies for the development of artificial pancreas by Atangana Baleanu derivative q , Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.04.027