A Caputo Fabrizio fractional order model for control of glucose in insulin therapies for diabetes
Tóm tắt
Từ khóa
Tài liệu tham khảo
World Health Organization; 2016. http://www.who.int/mediacentre/factsheets/fs312/en/ [accessed 23 Mar 2016].
Chee, 2007
Saleem, 2017, Control of an artificial human pancreas, Chin J Phys, 55, 2273, 10.1016/j.cjph.2017.08.030
Medtronic; 2016. http://www.medtronicdiabetes.com/products/continuous-glucose-monitoring [accessed 23 Mar 2016].
Sakulrang, 2017, A fractional differential equation model for continuous glucose monitoring data, Adv Differ Eqs, 2017, 150, 10.1186/s13662-017-1207-1
Reznik, 2010, Continuous subcutaneous insulin infusion (CSII) using an external insulin pump for the treatment of type 2 diabetes, Diabetes Metab, 36, 415, 10.1016/j.diabet.2010.08.002
Huang, 2012, Modeling impulsive injections of insulin: towards artificial pancreas, SIAM J Appl Math, 72, 1524, 10.1137/110860306
Song, 2014, Modeling impulsive insulin delivery in insulin pump with time delays, SIAM J Appl Math, 74, 1763, 10.1137/130933137
Shouzong, 2018, Finite-time control of plasma glucose in insulin therapies for diabetes, Adv Differ Eqs, 2018, 136, 10.1186/s13662-018-1532-z
Schmidt, 2015, The contribution of glucagon in an artificial pancreas for people with Type 1 diabetes 2015, Am Control Conf Palmer House Hilton, 1–3
Boiroux, 2014, Assessment of model predictive and adaptive glucose control strategies for people with type 1 diabetes
Farman, 2018, Stability analysis and control of glucose insulin glucagon system in human, Chines J Phys, 56, 1362, 10.1016/j.cjph.2018.03.037
Saleem, 2019, Stability analysis and control of fractional order diabetes mellitus model for artificial pancreas, Punjab Univ J Math, 51, 97
Saleem MU, Farman M, Rizwan M, MO Ahmad, Aqeel A, Controllability and observability of glucose insulin glucagon systems in human. Chines J Phys 2018; 56(5):1909–16.
Farman, 2019, A linear control of composite model for glucose insulin glucagon, Ain Shamas Eng J, 10, 867, 10.1016/j.asej.2019.04.001
Caputo, 1969
Podlubny, 1999
Baleanu D, Guvenc ZB, Tenreiro M, J.A. (eds.), New Trends in Nanotechnology and Fractional Calculus Applications. Springer, Dordrecht (2010)
Singh, 2018, A fractional epidemiological model for computer viruses pertaining to a new fractional derivative, Appl Math Comput, 316, 504
Singh, 2017, On the analysis of chemical kinetics system pertaining to a fractional derivative with Mittag-Leffler type kernel, Chaos, 27, 103, 10.1063/1.4995032
Kumar, 2018, Sushila, Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel, Physica A, 492, 155, 10.1016/j.physa.2017.10.002
Caputo, 2015, A new definition of fractional derivative without singular kernel, Prog Fract Differ Appl, 1, 73
Singh, 2018, On the analysis of fractional diabetes model with exponential law, Adv DifferEqs., 2018, 231, 10.1186/s13662-018-1680-1
Goharimanesh, 2015, Fractional order PID controller for diabetes patients, JAMECH, 46, 69
Changjin, 2019, Influence of time delay on bifurcation in fractional order BAM neural networks with four delays, IEEE Access, 7, 70955
Changjin, 2019, Bifurcation control for a fractional-order competition model of Internet with delays, Nonlinear Dyn, 95, 3335, 10.1007/s11071-018-04758-w
Li, 2018, Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations, Appl Math Comput, 324, 254
Ding, 2016, Global Mittag-Leffler synchronization of fractional-order neural networks with discontinuous activations, Neural Netw, 73, 77, 10.1016/j.neunet.2015.10.010
Wang, 2017, Uniqueness and existence of positive solutions for the fractional integro-differential equation, Bound Value Prob, 2017, 12, 10.1186/s13661-016-0741-1
Changjin, 2019, Influence of multiple time delays on bifurcation of fractional-order neural networks, Appl Math Comput, 361, 565
Zhang, 2017, Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition, Neural Netw, 94, 67, 10.1016/j.neunet.2017.06.010
Kilbas, 2006, vol. 204
Losada, 2015, Properties of the new fractional derivative without singular kernel, Prog Fract Differ Appl, 1, 8792
Sandhya, 2011, Mathematical model for glucose-insulin regulatory system of diabetes mellitus, Adv Appl Math Biosci, 2, 39
Hunter, 2001