A Systematic Investigation of the Fractional Biochemical Reaction Model via a Statistical Approach

Analyzing the Michaelis-Menten kinetics biochemical reaction model is essential in understanding enzyme-catalyzed reactions. Traditional models frequently fail to incorporate the complexities of fractional derivatives. This study employs the homotopy perturbation method (HPM) and the homotopy analysis method (HAM) to derive analytical expressions for enzyme, substrate, inhibitor, product, and other intermediate species concentrations. The methodologies include the application of fractional derivatives to improve the accuracy and adaptability of the model.The use of HPM and HAM in this context allows for a more comprehensive understanding of the biochemical reaction kinetics. The comparison of these two methodologies using numerical illustrations provides insights into their respective accuracies and applicability in biochemical modeling. Statistical analysis further strengthens the validation of these methods. Numerical examples demonstrate the effectiveness of HPM and HAM in dealing with the complexities associated with the Michaelis-Menten kinetics biochemical reaction model. The results highlight the improved precision in depicting the concentrations of various species within the reaction model. This study provides a comparison of the HAM findings with those produced by the HPM, demonstrating that the HAM approximate solutions are only valid for a short period, but the HPM results are very accurate and valid for a long time. This emphasizes the fact that the HPM applies to a wide range of nonlinear models and is reliable and promising when compared to other approaches. These approaches enhance the comprehension and application of biochemical reaction models, demonstrating efficacy through practical numerical results.