Computational analysis of fractional Michaelis-Menten enzymatic reaction model

Devendra Kumar; Hunney Nama; Dumitru Baleanu; Devendra Kumar; Hunney Nama; Dumitru Baleanu

doi:10.3934/math.2024033

AIMS Mathematics

2024, Volume 9, Issue 1: 625-641. doi: 10.3934/math.2024033

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Research article

Computational analysis of fractional Michaelis-Menten enzymatic reaction model

1.
Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India; namahunney99@gmail.com
2.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea
3.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; dumitru.baleanu@lau.edu.lb
4.
Institute of Space Sciences, Magurele-Bucharest, Romania

Received: 23 August 2023 Revised: 26 October 2023 Accepted: 29 October 2023 Published: 01 December 2023
MSC : 26A33, 33C45, 65L05

In this study for examining the fractional Michaelis-Menten enzymatic reaction (FMMER) model, we suggested a computational method by using an operational matrix of Jacobi polynomials (JPs) as its foundation. We obtain an operational matrix for the arbitrary order derivative in the Caputo sense. The fractional differential equations (FDEs) are then reduced to a set of algebraic equations by using attained operational matrix and the collocation method. The approach which utilized in this study is quicker and more effective compared to other schemes. We also compared the suggested method with the Vieta-Lukas collocation technique (VLCM) and we obtain excellent results. A comparison between numerical outcomes is shown by figures and tables. Error analysis of the recommended methods is also presented.
- FMMER,
- VLCM,
- Jacobi polynomials,
- FDEs,
- operational matrix,
- collocation technique
Citation: Devendra Kumar, Hunney Nama, Dumitru Baleanu. Computational analysis of fractional Michaelis-Menten enzymatic reaction model[J]. AIMS Mathematics, 2024, 9(1): 625-641. doi: 10.3934/math.2024033

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Abstract

In this study for examining the fractional Michaelis-Menten enzymatic reaction (FMMER) model, we suggested a computational method by using an operational matrix of Jacobi polynomials (JPs) as its foundation. We obtain an operational matrix for the arbitrary order derivative in the Caputo sense. The fractional differential equations (FDEs) are then reduced to a set of algebraic equations by using attained operational matrix and the collocation method. The approach which utilized in this study is quicker and more effective compared to other schemes. We also compared the suggested method with the Vieta-Lukas collocation technique (VLCM) and we obtain excellent results. A comparison between numerical outcomes is shown by figures and tables. Error analysis of the recommended methods is also presented.

References

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