Abstract
In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We construct three schema of successive approximations according to the theory of fractional calculus and with the help of Lagrange polynomials. The approximate solutions are compared with the resulting numerical solutions using the finite difference method (FDM). Because the approximate solutions in the classical case of the three models are very close to each other and almost matches, it is sufficient to compare one model, and the results were good. We investigate the effects of the fractal order and fractional order for all models. All calculations were performed using Mathematica software.
Highlights
Shateyi et al [1] proposed a method which is an extension of the spectral homotopy analysis method for investigating the approximate solution of the Michaelis–Menten enzymatic reaction equation
We illustrated the numerical results graphically through four figures via the the fractal–fractional Michaelis–Menten enzymatic reaction based on power law, exponential decay, and Mittag-Leffler kernels
We have proposed three new models of Michaelis–Menten enzymatic reaction by replacing the classical differential derivatives with fractal–fractional derivatives based on power law, exponential decay, and Mittag-Leffler kernels
Summary
Shateyi et al [1] proposed a method which is an extension of the spectral homotopy analysis method for investigating the approximate solution of the Michaelis–Menten enzymatic reaction equation. Abu-Reesh [2] derived analytical equations for the optimal design of a number of membrane reactors in series performing enzyme catalyzed reactions. This enzyme is described by Michaelis–Menten kinetics with competitive product inhibition. Golicnik [4] showed that analysis of the progress-curve data can be carried out through explicit mathematical equations; this analysis can be performed using any nonlinear regression-curve fitting program He found that when the progress curves are analyzed by the direct solution of the integrated
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