Comparative study of blood sugar–insulin model using fractional derivatives

References

• Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier; 1998.
   Google Scholar
• Caputo M. Linear models of dissipation whose Q is almost frequency independent–II. Geophys J Int. 1967;13(5):529–539. doi: 10.1111/j.1365-246X.1967.tb02303.x
   Web of Science ®Google Scholar
• Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations; 1993. (No Title).
   Google Scholar
• Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Vol. 204. Elsevier; 2006.
   Google Scholar
• Baleanu D, Diethelm K, Scalas E, et al. Fractional calculus: models and numerical methods. Vol. 3. World Scientific; 2012.
   Google Scholar
• Alkahtani BST, Atangana A. Analysis of non-homogeneous heat model with new trend of derivative with fractional order. Chaos Solit Fractals. 2016;89:566–571. doi: 10.1016/j.chaos.2016.03.027
   Web of Science ®Google Scholar
• Alqahtani AM, Mishra MN. Mathematical analysis of Streptococcus suis infection in pig–human population by Riemann–Liouville fractional operator. Prog Fract Differ Appl. 2024;10(1):119–135. doi: 10.18576/pfda
   Google Scholar
• Yang XJ, Srivastava HM, Cattani C. Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics. Rom Rep Phys. 2015;67(3):752–761.
   Web of Science ®Google Scholar
• Alazman I, Alkahtani BST, Mishra MN. Nonlinear complex dynamical analysis and solitary waves for the (3+ 1)-D nonlinear extended quantum Zakharov–Kuznetsov equation. Results Phys. 2024;58:Article ID 107432. doi: 10.1016/j.rinp.2024.107432
   Web of Science ®Google Scholar
• Chaurasia VBL, Dubey RS, Belgacem FBM. Fractional radial diffusion equation analytical solution via Hankel and Sumudu transforms. Int J Math Eng Sci Aerosp. 2012;3(2):1–10.
   Google Scholar
• Jajarmi A, Ghanbari B, Baleanu D. A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence. Chaos Interdisciplinary J Nonlinear Sci. 2019;29(9):Article ID 093111. doi: 10.1063/1.5112177
   Web of Science ®Google Scholar
• Bergman RN, Ider YZ, Bowden CR, et al. Quantitative estimation of insulin sensitivity. Am J Physiol Endocrinol Metab. 1979;236(6):Article ID E667. doi: 10.1152/ajpendo.1979.236.6.E667
   Google Scholar
• Bergman RN, Toffolo G, Bowden CR, et al. Minimal modeling, partition analysis, and identification of glucose disposal in animals and man. IEEE Trans Biom Eng. 1980;Article ID 12935.
   Google Scholar
• Alkahtani BS, Algahtani OJ, Dubey RS, et al. The solution of modified fractional Bergman's minimal blood glucose-insulin model. Entropy. 2017;19(5):114. doi: 10.3390/e19050114
   Web of Science ®Google Scholar
• Dubey RS, Belgacem FBM, Goswami P. Homotopy perturbation approximate solutions for Bergman's minimal blood glucose-insulin model. J Fractal Geometry Nonlinear Anal Med Bio (FGNAMB). 2016;2(3):1–6.
   Google Scholar
• Fisher ME. A semiclosed-loop algorithm for the control of blood glucose levels in diabetics. IEEE Trans Biomed Eng. 1991;38(1):57–61. doi: 10.1109/10.68209
   PubMed Web of Science ®Google Scholar
• Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl. 2015;1(2):73–85.
   Google Scholar
• Shrahili M, Dubey RS, Shafay A. Inclusion of fading memory to Banister model of changes in physical condition. Discret Contin Dyn Syst S. 2020;13:881.
   Google Scholar
• Katatbeh QD, Belgacem FBM. Applications of the Sumudu transform to fractional differential equations. Nonlinear Stud. 2011;18(1):99–112.
   Google Scholar
• Agarwal H, Mishra MN, Dubey RS. On fractional Caputo operator for the generalized glucose supply model via incomplete Aleph function. Int J Math Ind. 2024;Article ID 2450003.
   Google Scholar
• Khan MW, Abid M, Khan Q. Fractional order Bergman's minimal model – A better representation of blood glucose-insulin system. In: 2019 International Conference on Applied and Engineering Mathematics (ICAEM). IEEE; 2019. p. 68–73.
   Google Scholar
• Singh J, Kumar D, Baleanu D. A new analysis of fractional fish farm model associated with Mittag–Leffler-type kernel. Int J Biomath. 2020;13(02):Article ID 2050010. doi: 10.1142/S1793524520500102
   Google Scholar
• Baleanu D, Wu GC. Some further results of the Laplace transform for variable–order fractional difference equations. Fract Calc Appl Anal. 2019;22(6):1641–1654. doi: 10.1515/fca-2019-0084
   Web of Science ®Google Scholar
• Baleanu D, Etemad S, Rezapour S. A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions. Bound Value Probl. 2020;2020:1–16. doi: 10.1186/s13661-020-01361-0
   Web of Science ®Google Scholar
• Alqahtani AM, Shukla A. Computational analysis of multi-layered Navier–Stokes system by Atangana–Baleanu derivative. Appl Math Sci Eng. 2024;32(1):Article ID 2290723.
   Google Scholar
• Dubey RS, Baleanu D, Mishra MN, et al. Solution of modified Bergman minimal blood glucose–insulin model using Caputo–Fabrizio fractional derivative. CMES. 2021;128(3):1247–1263. doi: 10.32604/cmes.2021.015224
   Web of Science ®Google Scholar
• Jajarmi A, Yusuf A, Baleanu D, et al. A new fractional HRSV model and its optimal control: a non-singular operator approach. Phys A: Stat Mech Appl. 2020;547:Article ID 123860. doi: 10.1016/j.physa.2019.123860
   Google Scholar
• Shahmorad S, Ostadzad MH, Baleanu D. A Tau–like numerical method for solving fractional delay integro-differential equations. Appl Numer Math. 2020;151:322–336. doi: 10.1016/j.apnum.2020.01.006
   Web of Science ®Google Scholar
• Alshabanat A, Jleli M, Kumar S, et al. Generalization of Caputo–Fabrizio fractional derivative and applications to electrical circuits. Front Phys. 2020;8:64. doi: 10.3389/fphy.2020.00064
   Web of Science ®Google Scholar
• Aydogan SM, Baleanu D, Mohammadi H, et al. On the mathematical model of Rabies by using the fractional Caputo–Fabrizio derivative. Adv Differ Equ. 2020;2020(1):382. doi: 10.1186/s13662-020-02798-4
   Google Scholar
• Baleanu D, Mohammadi H, Rezapour S. Analysis of the model of HIV-1 infection of CD4+ T-cell with a new approach of fractional derivative. Adv Differ Equ. 2020;2020(1):1–17. doi: 10.1186/s13662-019-2438-0
   PubMed Web of Science ®Google Scholar
• Moore EJ, Sirisubtawee S, Koonprasert S. A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment. Adv Differ Equ. 2019;2019(1):1–20. doi: 10.1186/s13662-019-2138-9
   Google Scholar
• Saleem MU, Farman M, Ahmad MO, et al. Control of an artificial human pancreas. Chin J Phys. 2017;55(6):2273–2282. doi: 10.1016/j.cjph.2017.08.030
   Web of Science ®Google Scholar
• Farman M, Saleem MU, Ahmed MO, et al. Stability analysis and control of the glucose insulin glucagon system in humans. Chin J Phys. 2018;56(4):1362–1369. doi: 10.1016/j.cjph.2018.03.037
   Web of Science ®Google Scholar
• Sheikh NA, Ali F, Saqib M, et al. Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction. Results Phys. 2017;7:789–800. doi: 10.1016/j.rinp.2017.01.025
   Web of Science ®Google Scholar
• Pacini G, Bergman RN. MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test. Comput Methods Programs Biomed. 1986;23(2):113–122. doi: 10.1016/0169-2607(86)90106-9
   PubMed Web of Science ®Google Scholar
• Shaikh A, Tassaddiq A, Nisar KS, et al. Analysis of differential equations involving Caputo–Fabrizio fractional operator and its applications to reaction–diffusion equations. Adv Differ Equ. 2019;2019(1):1–14. doi: 10.1186/s13662-019-2115-3
   Google Scholar
• Tarasov VE. Caputo–Fabrizio operator in terms of integer derivatives: memory or distributed lag?. Comput Appl Math. 2019;38:1–15. doi: 10.1007/s40314-019-0767-y
   Google Scholar
• Qureshi S, Rangaig NA, Baleanu D. New numerical aspects of Caputo–Fabrizio fractional derivative operator. Mathematics. 2019;7(4):374. doi: 10.3390/math7040374
   Web of Science ®Google Scholar
• Albalawi KS, Mishra MN, Goswami P. Analysis of the multi-dimensional Navier–Stokes equation by Caputo fractional operator. Fractal Fract. 2022;6(12):743. doi: 10.3390/fractalfract6120743
   Web of Science ®Google Scholar
• Kumawat N, Shukla A, Mishra MN, et al. Khalouta transform and applications to Caputo-fractional differential equations. Front Appl Math Stat. 2024;10:Article ID 1351526. doi: 10.3389/fams.2024.1351526
   Google Scholar
• Dubey RS, Mishra MN, Goswami P. Effect of Covid-19 in India–A prediction through mathematical modeling using Atangana Baleanu fractional derivative. J Interdiscip Math. 2022;25(8):2431–2444. doi: 10.1080/09720502.2021.1978682
   Web of Science ®Google Scholar
• Fatmawati K, Alzahrani E. Analysis of dengue model with fractal–fractional Caputo–Fabrizio operator. Adv Differ Equ. 2020;2020(1):422. doi: 10.1186/s13662-020-02881-w
   Web of Science ®Google Scholar
• Losada J, Nieto JJ. Properties of a new fractional derivative without singular kernel. Progr Fract Differ Appl. 2015;1(2):87–92.
   Google Scholar
• Mishra MN, Aljohani AF. Mathematical modelling of growth of tumour cells with chemotherapeutic cells by using Yang–Abdel–Cattani fractional derivative operator. J Taibah Univ Sci. 2022;16(1):1133–1141. doi: 10.1080/16583655.2022.2146572
   Web of Science ®Google Scholar