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

Ritu Agarwal; Pooja Airan; Mohammad Sajid; Ritu Agarwal; Pooja Airan; Mohammad Sajid

doi:10.3934/mbe.2024227

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5138-5163. doi: 10.3934/mbe.2024227

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

1.
Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India
2.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia

Received: 01 January 2024 Revised: 13 February 2024 Accepted: 20 February 2024 Published: 04 March 2024

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.
- bone mineralization,
- Caputo-Fabrizio fractional derivative,
- mathematical model,
- simulation,
- numerical solutions,
- stability analysis
Citation: Ritu Agarwal, Pooja Airan, Mohammad Sajid. Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5138-5163. doi: 10.3934/mbe.2024227

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Abstract

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.

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