Modeling continuous glucose monitoring with fractional differential equations subject to shocks

Gaetano, Andrea De; Sakulrang, Sasikarn; Borri, Alessandro; Pitocco, Dario; Sungnul, Surattana; Moore, Elvin J.

doi:10.1016/j.jtbi.2021.110776

Cited by 8 publications

(3 citation statements)

References 29 publications

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“…Also, the new equalities in this manuscript could be used in many other topics. Fractional calculus is frequently applied in other fields of sciences and medicine, as it could be seen that it was used for modeling in various areas [15][16][17][18][19][20]. We believe that the relations in this manuscript could be used in different disciplines in the future.…”

Section: Discussionmentioning

confidence: 97%

Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

Albayrak

Dernek

2023

Gazi University Journal of Science

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Section: Discussionmentioning

confidence: 97%

Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

Albayrak

Dernek

2023

Gazi University Journal of Science

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“…Fractional calculus is the research of integrals and derivatives of any arbitrary real or complex order. In recent years, fractional differential equations have been acquired much attention due to its applications in a number of fields such as fluid flow, control theory of dynamical systems, chemistry, biology, optics and signal processing [1][2][3][4][5][6][7][8][9][10][11]. For example, Mohammadi et al [8] proposed a fractional differential equations model for hearing loss due to mumps virus:…”

Section: Introductionmentioning

confidence: 99%

Untitled

Nan¹,

Hu²,

Su³

et al. 2023

DSA

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As we all know, star graphs are very useful in physics, chemistry, biology and other fields, but few people have studied the existence of solutions to differential system on star graphs.In this paper, we investigate the existence of solutions to a fractional differential system on star graphs with p-Laplacian operator. Ulam's stability and existence of the solutions to the fractional differential system on star graphs are proved. In addition, two examples under different background graphs (star graphs and formaldehyde graphs) and the approximation graphics for the solutions are provided to illustrate the application of our main results. The interesting point of this article is that it not only studies the existence of solutions to fractional differential system on the star graphs, but also gives approximate graphs of solutions by using the iterative methods and numerical simulation.

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“…The study also estimated unknown model parameters based on samples which were collected from the patient with non-small cell lung cancer who had chemotherapy-naive hospitalized. De Gaetano et al [ 5 ] presented a mathematical model with a fractional derivative for Continuous Glucose Monitoring. The paper also contains the numerical solution of the considered fractional model.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Heuristic Algorithms in Identification of Parameters of Anomalous Diffusion Model Based on Measurements from Sensors

Brociek

Wajda²,

Słota

2023

Sensors

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In recent times, fractional calculus has gained popularity in various types of engineering applications. Very often, the mathematical model describing a given phenomenon consists of a differential equation with a fractional derivative. As numerous studies present, the use of the fractional derivative instead of the classical derivative allows for more accurate modeling of some processes. A numerical solution of anomalous heat conduction equation with Riemann-Liouville fractional derivative over space is presented in this paper. First, a differential scheme is provided to solve the direct problem. Then, the inverse problem is considered, which consists in identifying model parameters such as: thermal conductivity, order of derivative and heat transfer. Data on the basis of which the inverse problem is solved are the temperature values on the right boundary of the considered space. To solve the problem a functional describing the error of the solution is created. By determining the minimum of this functional, unknown parameters of the model are identified. In order to find a solution, selected heuristic algorithms are presented and compared. The following meta-heuristic algorithms are described and used in the paper: Ant Colony Optimization (ACO) for continous function, Butterfly Optimization Algorithm (BOA), Dynamic Butterfly Optimization Algorithm (DBOA) and Aquila Optimize (AO). The accuracy of the presented algorithms is illustrated by examples.

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Modeling continuous glucose monitoring with fractional differential equations subject to shocks

Cited by 8 publications

References 29 publications

Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

Untitled

Comparison of Heuristic Algorithms in Identification of Parameters of Anomalous Diffusion Model Based on Measurements from Sensors

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