Analysis and controllability of diabetes model for experimental data by using fractional operator

Farman, Muhammad; Ahmad, Aqeel; Zehra, Anum; Nisar, Kottakkaran Sooppy; Hincal, Evren; Akgul, Ali

doi:10.1016/j.matcom.2023.11.017

Cited by 14 publications

(3 citation statements)

References 23 publications

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“…Farman et al [26] put out a mathematical model that includes the fractional operator and includes β−cells, insulin, glucose, and growth hormone. We handled a global stability analysis using the Lyapunov function and looked at how a new wave of dynamical transmission affected the second derivative's equilibrium points.…”

Section: Introductionmentioning

confidence: 99%

A vibration analysis of the permanent magnet synchronous motor under the effect of proportional derivative control

Bauomy,

Amer,

Elsayed

et al. 2024

Phys. Scr.

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One of the drawbacks of the electric motor is that it starts overheating after a short time. The reason can be associated with oscillating vibration, so the present study uses a proportional derivative control (PD control) to show the extent to which the Permanent magnet synchronous motor (PMSM) can be effective.The external force is the component of the non-linear dynamical system. The equation of the (PMSM) system is explained with two-degree-of-freedom (2dof) differential coupled equations, consisting of the major body (motor current) and the cutting drive system. The present study uses the approximate method of multiple scales perturbation technique (MSPT) to get an approximate solution, showing the response equation before using (PD) and to achieve the highest effect on the control system so as to ensure the highest efficiency at the lowest possible cost. Different numerical tests have been conducted (NPDCVF, NVC, PPF, PD, delay velocity) and showed that (PD) has the best effect and is able to control the vibrations with more accuracy than others. Then, the vibration value of the system has been studied numerically before and after applying the control method of (MSPT). By combining the analysis of the resonance situation via both the phase plane techniques and the frequency response equation    1  2,  2  , within the utilization of Runge-Kutta of the fourth-order, the stability of the numerical solution has been investigated. Then, by employing the MATLAB tool, the impact of various parameters on model performance has been examined numerically. Lastly, a comparison with earlier research is done.

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Section: Introductionmentioning

confidence: 99%

A vibration analysis of the permanent magnet synchronous motor under the effect of proportional derivative control

Bauomy,

Amer,

Elsayed

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Diabetes is a complex physiological condition characterized by disrupted insulin production and utilization, leading to elevated blood glucose levels [1][2][3]. It is categorized into two primary types: Type 1 and Type 2 [4,5]. In Type 1 diabetes, the pancreatic β-cells responsible for insulin regulation are progressively destroyed, rendering precise blood glucose management elusive [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Optimizing Blood Glucose Regulation in Type 1 Diabetes Patients via Genetic Algorithm-Based Fuzzy Logic Controller Considering Substantial Meal Protocol

Ndakara Abubakar,

Essabbar,

Saikouk

2024

Int. J. Onl. Eng.

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Effective management of blood glucose levels in individuals with type 1 diabetes, especially after meals, is crucial for diabetes care. Artificial pancreas systems (APS) perform automated insulin delivery in subjects with type 1 diabetes mellitus (T1DM). In this study, an optimized fuzzy logic controller was designed to achieve a euglycemic range after a substantial meal intake. All in silico simulations were performed using the MATLAB/Simulink environment, leveraging control variability grid analysis (CVGA), and the performance of the controller was evaluated. The proposed controller is based on a fuzzy-logic control law designed in three stages. First, a nonlinear framework of the glucose-insulin regulatory system was identified based on the heavy meal protocol of three patients given as follows: for subject ID 117-1, a total of 295 gCHO; for subject ID 126-1, 236 gCHO; and subject ID 128-1, 394 gCHO over a day. Then, an iterative tree structure was employed to establish a stabilizing control rule for insulin delivery, integrating inputs from two Mamdani Fuzzy Inference System (FIS) objects. Finally, a genetic algorithm refines the control system by fine-tuning the uncertainty of the fuzzy membership functions. Two scenarios were considered for three patients to assess the performance of the proposed controller. The results indicated its effectiveness under various conditions, achieving a time in the range of 61.25%, 71% and 61.10% respectively for the three subjects. The obtained results are analyzed and compared with IMC and multi-objective output feedback controllers. The findings of the study reveal that the proposed controller shows promising advancements in tailored strategies for type 1 diabetes patients, outperforming the other controllers in terms of blood glucose regulation.

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“…Te researchers point out in [4] that the model can predict the course of infection and the efectiveness of diferent treatment strategies. It can also be used to understand the disease's mechanisms and identify potential targets for new therapies [5,6]. Many fractional diferential operators have been used in so-called mathematical epidemiology to model many infectious diseases as mathematical models of infectious diseases are important sources for understanding and interpreting the dynamics of those diseases such as coronaries, polycystic ovarian syndrome, tuberculosis, immunodefciency, infuenza, cancer, and hepatitis [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

Salah,

Sontakke,

Abdo

et al. 2024

International Journal of Differential Equations

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The mathematical model of the dynamics of HIV/AIDS infection transmission is developed by adding the set of infected but noninfectious persons, using a conformable fractional derivative in the Liouville–Caputo sense. Some fixed point theorems are applied to this model to investigate the existence and uniqueness of the solutions. It is determined what the system’s fundamental reproduction number R0 is. The disease-free equilibrium displays the model’s stability and the local stability around the equilibrium. The study also examined the effects of different biological features on the system through numerical simulations using the Adams–Moulton approach. Additionally, varied values of fractional orders are simulated numerically, demonstrating that the results generated by the conformable fractional derivative-based model are more physiologically plausible than integer-order derivatives.

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Analysis and controllability of diabetes model for experimental data by using fractional operator

Cited by 14 publications

References 23 publications

A vibration analysis of the permanent magnet synchronous motor under the effect of proportional derivative control

A vibration analysis of the permanent magnet synchronous motor under the effect of proportional derivative control

Optimizing Blood Glucose Regulation in Type 1 Diabetes Patients via Genetic Algorithm-Based Fuzzy Logic Controller Considering Substantial Meal Protocol

Conformable Fractional-Order Modeling and Analysis of HIV/AIDS Transmission Dynamics

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