ANALYTIC SOLUTION OF ONE-DIMENSIONAL FRACTIONAL GLYCOLYSIS MODEL

Faiz Muhammad Khan, Amjad Ali, Abdullah, Ilyas Khan, Abha Singh and Sayed M. Eldin
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Faiz Muhammad Khan: Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan
Amjad Ali: Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan
Abdullah: Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan
Ilyas Khan: ��Department of Mathematics, College of Science, Al-Zulfi Majmaah University, Al-Majma’ah 11952, Saudi Arabia
Abha Singh: ��Department of Basic Sciences, College of Sciences and Theoretical Studies, Dammam-branch, Saudi Electronic University, Riyadh, Saudi Arabia
Sayed M. Eldin: �Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-7

Abstract: Glycolysis, which occurs in the cytoplasm of both prokaryotic and eukaryotic cells, is regarded to be the primary step employed in the breakdown of glucose to extract energy. As it is utilized by all living things on the planet, it was likely one of the first metabolic routes to emerge. It is a cytoplasmic mechanism that converts glucose into carbon molecules while also producing energy. The enzyme hexokinase aids in the phosphorylation of glucose. Hexokinase is inhibited by this mechanism, which generates glucose-6-P from adenosine triphosphate (ATP). This paper’s primary goal is to quantitatively examine the general reaction–diffusion Glycolysis system. Since the Glycolysis model shows a positive result as the unknown variables represent chemical substance concentration, therefore, to evaluate the behavior of the model for the non-integral order derivative of both independent variables, we expanded the concept of the conventional order Glycolysis model to the fractional Glycolysis model. The nonlinearity of the model is decomposed through an Adomian polynomial for evaluation. More precisely, we used the iterative Laplace Adomian decomposition method (LADM) to determine the numerical solution for the underlying model. The model’s necessary analytical/numerical solution was found by adding the first few iterations. Finally, we have presented numerical examples and graphical representations to explain the dynamics of the considered model to ensure the scheme’s validity.

Keywords: Fractional Derivative; Glycolysis Model; Approximate Solution; Laplace Transform; Mathematica (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23402016

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