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<p>The dynamics of a non-linear fractional-order chemical reaction model that describes the interactions between an enzyme, substrate, inhibitor and the related intermediate complexes are examined in this paper. Iterative numerical simulations are used to derive analytical approximations using the Homotopy Analysis Method (HAM) and the Homotopy Perturbation Method (HPM). The fractional-order model indicates that the concentrations of free enzyme and inhibitor decrease gradually and the concentration of substrate remains relatively constant over the time period. The enzyme-substrate conversion is represented by the monotonic growth of product concentration. Among the intermediates, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C_1(t)\)</EquationSource> </InlineEquation> varies slightly, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C_2(t)\)</EquationSource> </InlineEquation> reaches relatively higher values and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C_3(t)\)</EquationSource> </InlineEquation> is relatively small, as expected from the reaction schemes described by the model. Both HAM and HPM are successful in describing the overall kinetic behaviour of the system. Error analysis reveals that both approaches are better for different components of the system, with improved agreement of HPM for some components and better convergence properties of HAM. The findings demonstrate that both semi-analytical approaches are reliable and efficient tools for solving nonlinear fractional-order chemical kinetic systems and the numerical approximation provides a trustworthy benchmark.</p>

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Numerical analysis of non-linear complex biochemical reaction model using HPM and HAM

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • L. Dhanuja,
  • C. Monica

摘要

The dynamics of a non-linear fractional-order chemical reaction model that describes the interactions between an enzyme, substrate, inhibitor and the related intermediate complexes are examined in this paper. Iterative numerical simulations are used to derive analytical approximations using the Homotopy Analysis Method (HAM) and the Homotopy Perturbation Method (HPM). The fractional-order model indicates that the concentrations of free enzyme and inhibitor decrease gradually and the concentration of substrate remains relatively constant over the time period. The enzyme-substrate conversion is represented by the monotonic growth of product concentration. Among the intermediates, \(C_1(t)\) varies slightly, \(C_2(t)\) reaches relatively higher values and \(C_3(t)\) is relatively small, as expected from the reaction schemes described by the model. Both HAM and HPM are successful in describing the overall kinetic behaviour of the system. Error analysis reveals that both approaches are better for different components of the system, with improved agreement of HPM for some components and better convergence properties of HAM. The findings demonstrate that both semi-analytical approaches are reliable and efficient tools for solving nonlinear fractional-order chemical kinetic systems and the numerical approximation provides a trustworthy benchmark.