Dynamics of enzyme kinetic model under the new generalized Hattaf fractional derivative

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dc.citation.epage469
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та обчислення
dc.citation.spage463
dc.citation.volume11
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationРегіональний центр освіти і підготовки професій (CRMEF)
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.affiliationCentre R´egional des M´etiers de l’Education et de la Formation (CRMEF)
dc.contributor.authorЕль Мамуні, Х.
dc.contributor.authorХаттаф, К.
dc.contributor.authorЮсфі, Н.
dc.contributor.authorEl Mamouni, H.
dc.contributor.authorHattaf, K.
dc.contributor.authorYousfi, N.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T08:10:19Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractКаталітична дія є однією з найважливіших характеристик ферментів у хімічних реакціях. У цій статті пропонується та досліджується математична модель хімічної кінетичної реакції з ефектом пам’яті з використанням нової узагальненої дробової похідної Хаттафа. Існування та єдиність розв’язків встановлено за допомогою теорії нерухомої точки, і, нарешті, щоб підтвердити теоретичні результати, закінчуємо чисельним моделюванням на основі нової чисельної схеми, яка включає метод Ейлера.
dc.description.abstractCatalytic action is one of the most important characteristics of enzymes in chemical reactions. In this article, we propose and study a mathematical model of chemical kinetic reaction with the memory effect using the new generalized Hattaf fractional derivative. The existence and uniqueness of the solutions are established by means of fixed point theory and, finally, to support the theoretical results, we end the article with the results of numerical simulations based on a novel numerical scheme that includes the Euler method.
dc.format.extent463-469
dc.format.pages7
dc.identifier.citationEl Mamouni H. Dynamics of enzyme kinetic model under the new generalized Hattaf fractional derivative / H. El Mamouni, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 463–469.
dc.identifier.citationenEl Mamouni H. Dynamics of enzyme kinetic model under the new generalized Hattaf fractional derivative / H. El Mamouni, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 463–469.
dc.identifier.doidoi.org/10.23939/mmc2024.02.463
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113806
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та обчислення, 2 (11), 2024
dc.relation.ispartofMathematical Modeling and Computing, 2 (11), 2024
dc.relation.references[1] Wong J. T.-F. Onthe Steady-State Method of Enzyme Kinetics. Journalof the AmericanChemical Society. 87 (8), 1788–1793 (1965).
dc.relation.references[2] Michaelis L., Menten M. L. Die Kinetik der Invertinwirkung. Biochemische Zeitschrift. 49, 333–369 (1913).
dc.relation.references[3] Cha S. Kinetic Behavior at High Enzyme Concentrations: Magnitude of errors of michaelis-menten and other approximations. Journal of Biological Chemistry. 245 (18), 4814–4818 (1970).
dc.relation.references[4] Wald S., Wilke C. R., Blanch H. W. Kinetics of the enzymatic hydrolysis of cellulose. Biotechnology and Bioengineering. 26 (3), 221–230 (1984).
dc.relation.references[5] Najafpour G. D., Shan C. P. Enzymatic hydrolysis of molasses. Bioresource Technology. 86 (1), 91–94 (2003).
dc.relation.references[6] Gan Q., Allen S. J., Taylor G. Kinetic dynamics in heterogeneous enzymatic hydrolysis of cellulose: an overview, an experimental study and mathematical modelling. Process Biochemistry. 38 (7), 1003–1018 (2003).
dc.relation.references[7] Urban P. L., Goodall D. M., Bruce N. C. Enzymatic microreactors in chemical analysis and kinetic studies. Biotechnology Advances. 24 (1), 42–57 (2006).
dc.relation.references[8] Wong M. K. L., Krycer J. R., Burchfield J. G., James D. E., Kuncic Z. A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems. FEBS Open Bio. 5 (1), 226–239 (2015).
dc.relation.references[9] Atangana A. Modeling the Enzyme Kinetic Reaction. Acta Biotheoretica. 63, 239–256 (2015).
dc.relation.references[10] Milek J. Estimation of the Kinetic Parameters for H2O2 Enzymatic decomposition and for catalase deactivation. Brazilian Journal of Chemical Engineering. 35 (3), 995–1004 (2018).
dc.relation.references[11] Khan M., Ahmed Z., Ali F., Khan N., Khan I., Nisar K. S. Dynamics of two-step reversible enzymatic reaction with Mittag–Leffler Kernel. PLoS ONE. 18 (3), e0277806 (2023).
dc.relation.references[12] Atangana A., Baleanu D. New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science. 20 (2), 763–769 (2016).
dc.relation.references[13] Hattaf K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8 (2), 49 (2020).
dc.relation.references[14] Caputo A., Fabrizio M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications. 1 (2), 73–85 (2015).
dc.relation.references[15] Al-Refai M. On weighted Atangana–Baleanufractional operators. Advances in Difference Equations. 2020, 3 (2020).
dc.relation.references[16] Djida J. D., Atangana A., Area I. Numerical Computation of a Fractional Derivative with Non-Local and Non-Singular Kernel. Mathematical Modelling of Natural Phenomena. 12 (3), 4–13 (2017).
dc.relation.references[17] Baleanu D., Fernandez A. On some new properties of fractional derivatives with Mittag–Leffler kernel. Communications in Nonlinear Science and Numerical Simulation. 59, 444–462 (2018).
dc.relation.references[18] Hattaf K. On some properties of the new generalized fractional derivative with non-singular kernel. Mathematical Problems in Engineering. 2021, 1580396 (2021).
dc.relation.references[19] Hattaf K. On the Stability and Numerical Scheme of Fractional Differential Equations with Application to Biology. Computation. 10 (6), 97 (2022).
dc.relation.referencesen[1] Wong J. T.-F. Onthe Steady-State Method of Enzyme Kinetics. Journalof the AmericanChemical Society. 87 (8), 1788–1793 (1965).
dc.relation.referencesen[2] Michaelis L., Menten M. L. Die Kinetik der Invertinwirkung. Biochemische Zeitschrift. 49, 333–369 (1913).
dc.relation.referencesen[3] Cha S. Kinetic Behavior at High Enzyme Concentrations: Magnitude of errors of michaelis-menten and other approximations. Journal of Biological Chemistry. 245 (18), 4814–4818 (1970).
dc.relation.referencesen[4] Wald S., Wilke C. R., Blanch H. W. Kinetics of the enzymatic hydrolysis of cellulose. Biotechnology and Bioengineering. 26 (3), 221–230 (1984).
dc.relation.referencesen[5] Najafpour G. D., Shan C. P. Enzymatic hydrolysis of molasses. Bioresource Technology. 86 (1), 91–94 (2003).
dc.relation.referencesen[6] Gan Q., Allen S. J., Taylor G. Kinetic dynamics in heterogeneous enzymatic hydrolysis of cellulose: an overview, an experimental study and mathematical modelling. Process Biochemistry. 38 (7), 1003–1018 (2003).
dc.relation.referencesen[7] Urban P. L., Goodall D. M., Bruce N. C. Enzymatic microreactors in chemical analysis and kinetic studies. Biotechnology Advances. 24 (1), 42–57 (2006).
dc.relation.referencesen[8] Wong M. K. L., Krycer J. R., Burchfield J. G., James D. E., Kuncic Z. A generalised enzyme kinetic model for predicting the behaviour of complex biochemical systems. FEBS Open Bio. 5 (1), 226–239 (2015).
dc.relation.referencesen[9] Atangana A. Modeling the Enzyme Kinetic Reaction. Acta Biotheoretica. 63, 239–256 (2015).
dc.relation.referencesen[10] Milek J. Estimation of the Kinetic Parameters for H2O2 Enzymatic decomposition and for catalase deactivation. Brazilian Journal of Chemical Engineering. 35 (3), 995–1004 (2018).
dc.relation.referencesen[11] Khan M., Ahmed Z., Ali F., Khan N., Khan I., Nisar K. S. Dynamics of two-step reversible enzymatic reaction with Mittag–Leffler Kernel. PLoS ONE. 18 (3), e0277806 (2023).
dc.relation.referencesen[12] Atangana A., Baleanu D. New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science. 20 (2), 763–769 (2016).
dc.relation.referencesen[13] Hattaf K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8 (2), 49 (2020).
dc.relation.referencesen[14] Caputo A., Fabrizio M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications. 1 (2), 73–85 (2015).
dc.relation.referencesen[15] Al-Refai M. On weighted Atangana–Baleanufractional operators. Advances in Difference Equations. 2020, 3 (2020).
dc.relation.referencesen[16] Djida J. D., Atangana A., Area I. Numerical Computation of a Fractional Derivative with Non-Local and Non-Singular Kernel. Mathematical Modelling of Natural Phenomena. 12 (3), 4–13 (2017).
dc.relation.referencesen[17] Baleanu D., Fernandez A. On some new properties of fractional derivatives with Mittag–Leffler kernel. Communications in Nonlinear Science and Numerical Simulation. 59, 444–462 (2018).
dc.relation.referencesen[18] Hattaf K. On some properties of the new generalized fractional derivative with non-singular kernel. Mathematical Problems in Engineering. 2021, 1580396 (2021).
dc.relation.referencesen[19] Hattaf K. On the Stability and Numerical Scheme of Fractional Differential Equations with Application to Biology. Computation. 10 (6), 97 (2022).
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectферментативна реакція
dc.subjectдробова похідна Хаттафа
dc.subjectтеорія нерухомої точки
dc.subjectчисельне моделювання
dc.subjectenzymatic reaction
dc.subjectHattaf fractional derivative
dc.subjectfixed point theory
dc.subjectnumerical simulations
dc.titleDynamics of enzyme kinetic model under the new generalized Hattaf fractional derivative
dc.title.alternativeДинаміка ферментативної кінетичної моделі за новою узагальненою дробовою похідною Хаттафа
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 2