Solution of a Complex Nonlinear Fractional Biochemical Reaction Model

Rabah, Fatima; Abukhaled, Marwan; Khuri, Sami

doi:10.3390/mca27030045

Cited by 10 publications

(6 citation statements)

References 39 publications

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“…Fractional differential equations have gained prominence in recent research, serving as effective tools to model natural phenomena in various fields, including biological systems, 15,16 infectious diseases, 17,18 fluid flow, 19 biochemical reactions, 20 and control theory. 21 Due to the inherent nonlocal property of fractional derivative operators, fractional models prove adept at describing memory and hereditary properties of various materials and processes.…”

Section: Introductionmentioning

confidence: 99%

“…28,29 While these meth-ods demonstrated efficiency and accuracy, they are not without challenges, such as issues of numerical schemes and the necessity to adjust parameters to align with numerical data. 30 Among the analytical methods recently applied to solve fractional-derivative equations are the homotopy analysis method, 31 homotopy perturbation method, 32 differential transform method, 33 Green's function-fixed point method, 34 and cubic spline method. 35 These methods contribute to the expanding toolkit for dealing with the complexities inherent in nonlinear fractional-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Efficient semianalytical investigation of a fractional model describing human cornea shape

Abukhaled,

Abukhaled

2024

MAIO

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Purpose: This study presents a novel application of the semianalytical residual power series method to investigate a one-dimensional fractional anisotropic curvature equation describing the human cornea, the outermost layer of the eye. The fractional boundary value problem, involving the fractional derivative of curvature, poses challenges that conventional methods struggle to address. Methods: The analytical results are obtained by utilizing the simple and efficient residual power series method. The proposed method is accessible to researchers in all medical fields and is extendable to various models in disease spread and control. Results: The derived solution is a crucial outcome of this study. Through the application of the proposed method to the corneal shape model, an explicit formula for the curvature profile is obtained. To validate the solution, direct comparisons are made with numerical solutions for the integer case and other analytical solutions available in the literature for the fractional case. Conclusion: Our findings highlight the potential of the proposed method to significantly contribute to the diagnosis and treatment of various ophthalmological conditions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient semianalytical investigation of a fractional model describing human cornea shape

Abukhaled,

Abukhaled

2024

MAIO

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“…The goal of the fractional order, as well as significant reaction parameters on the enzymatic reaction, is to solve the fractional-order differential biochemical reaction model. Because it is difficult to find an accurate solution for every FDE, it is necessary to employ various numerical approaches [1,11,29]. Recently, several researchers discussed various mathematical models in [4,26,35].…”

Section: Introductionmentioning

confidence: 99%

A study of nonlinear fractional-order biochemical reaction model and numerical simulations

Radhakrishnan,

Chandru,

Nieto

2024

NAMC

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This article depicts an approximate solution of systems of nonlinear fractional biochemical reactions for the Michaelis–Menten enzyme kinetic model arising from the enzymatic reaction process. This present work is concerned with fundamental enzyme kinetics, utilised to assess the efficacy of powerful mathematical approaches such as the homotopy perturbation method (HPM), homotopy analysis method (HAM), and homotopy analysis transform method (HATM) to get the approximate solutions of the biochemical reaction model with time-fractional derivatives. The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. The comparison results reveal the complexity of the enzyme process and obtain approximate solutions to the nonlinear fractional differential biochemical reaction model.

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“…Other methods were proposed to handle fractional differential equations, such as Sakar et al (2018), who acquired very accurate numerical solutions of fractional Bratu-type equations by applying a Legendre reproducing kernel method. Other methods include Sinc-Galerkin method (Alkan, 2014), Quasi-Newton’s method (Jia et al , 2016) and Laplace differential transform method (Abukhaled et al , 2022; Rabah et al , 2022). To learn more about the different methods for solving ordinary and fractional differential equations, see Abukhaled (2013), Khuri and Sayfy (2014), Deeba and Khuri (1996), Shawagfeh (2002) and Wu (2011) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An extended variational iteration method for fractional BVPs encountered in engineering applications

Khuri

Assadi

2023

HFF

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Purpose The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications. Design/methodology/approach A newly developed semi-analytical scheme will be applied to find approximate solutions for fractional order boundary value problems. The technique is regarded as an extension of the well-established variation iteration method, which was originally proposed for initial value problems, to cover a class of boundary value problems. Findings It has been demonstrated that the method yields approximations that are extremely accurate and have uniform distributions of error throughout their domain. The numerical examples confirm the method’s validity and relatively fast convergence. Originality/value The generalized variational iteration method that is presented in this study is a novel strategy that can handle fractional boundary value problem more effectively than the classical variational iteration method, which was designed for initial value problems.

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Solution of a Complex Nonlinear Fractional Biochemical Reaction Model

Cited by 10 publications

References 39 publications

Efficient semianalytical investigation of a fractional model describing human cornea shape

Efficient semianalytical investigation of a fractional model describing human cornea shape

A study of nonlinear fractional-order biochemical reaction model and numerical simulations

An extended variational iteration method for fractional BVPs encountered in engineering applications

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