Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization

被引：2

作者：

Agarwal R. ^{[1
]}

Airan P. ^{[1
]}

Sajid M. ^{[2
]}

机构：

[1] Department of Mathematics, Malaviya National Institute of Technology, Jaipur

[2] Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah

来源：

Mathematical Biosciences and Engineering | 2024年 / 21卷 / 04期

关键词：

bone mineralization; Caputo-Fabrizio fractional derivative; mathematical model; numerical solutions; simulation; stability analysis;

D O I：

10.3934/mbe.2024227

中图分类号：

学科分类号：

摘要：

The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization. © 2024 the Author(s).

引用

页码：5138 / 5163

页数：25

共 32 条

[1]

Liu L., Chen S., Small M., Moore J. M., Shang K., Global stability and optimal control of epidemics in heterogeneously structured populations exhibiting adaptive behavior, Commun. Nonlinear Sci. Numer. Simul, 126, (2023)

[2]

Baleanu D., Diethelm K., Scalas E., Trujillo J. J., Fract. Calculus Models Numer. Methods, 3, (2012)

[3]

Diethelm K., Ford N. J., Analysis of fractional di_erential equations, J. Math. Anal. Appl, 265, pp. 229-248, (2002)

[4]

Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory Appl. Fract. Di_er. Equat, 204, (2006)

[5]

Abdulwasaa M. A., Abdo M. S., Shah K., Nofal T. A., Panchal S. K., Kawale S. V., Et al., Fractalfractional mathematical modeling and forecasting of new cases and deaths of COVID-19 epidemic outbreaks in India, Results Phys, 20, (2021)

[6]

Dhar B., Gupta P. K., Sajid M., Solution of a dynamical memory e_ect COVID-19 infection system with leaky vaccination e_cacy by non-singular kernel fractional derivatives, Math. Biosci. Eng, 19, pp. 4341-4367, (2022)

[7]

Agarwal R., Jain S., Agarwal R. P., Mathematical modeling and analysis of dynamics of cytosolic calcium ion in astrocytes using fractional calculus, J. Fract. Calculus Appl, 9, pp. 1-12, (2018)

[8]

Agarwal R., Kritika S. D., Kumar D., Mathematical modelling of cytosolic calcium concentration distribution using non-local fractional operator, Discrete Contin. Dynam. Syst.-S, 14, pp. 3387-3399, (2021)

[9]

Pandey R. M., Chandola A., Agarwal R., Mathematical model and interpretation of crowding e_ects on SARS-CoV-2 using Atangana-Baleanu fractional operator, Methods of Mathematical Modeling, pp. 41-58, (2022)

[10]

Mishra J., Agarwal R., Atangana A., Math. Model. Soft Comput. Epidemiol, (2020)

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