Wavelet-based mathematical analysis of immobilized enzymes in porous catalysts under nonlinear Michaelis–Menten kinetics

Immobilized enzymes in porous catalysts, such as spheres, cylinders, and flat pellets, with nonlinear Michaelis–Menten kinetics find widespread use in the food industry. This study introduces an efficient approach that applies wavelet-based spectrum analysis to explore the behavior of these immobilized enzymes. The models employed here are built upon nonlinear reaction–diffusion equations that include the nonlinear terms associated with Michaelis–Menten kinetics. Furthermore, this research delves into the enzymatic reaction kinetics using fractional derivatives, addressing a gap in the existing literature. To analyze this kinetic mechanism, the study employs the Hermite wavelet method (HWM) to examine analytical substrate concentration solutions and the effectiveness factor across various parameter values. The proposed analytical solutions based on Hermite wavelets are validated through numerical simulations in Matlab as well as compared with the Taylor series method (TSM) and the Adomian decomposition method (ADM), demonstrating excellent agreement with both semi-analytical and numerical solutions.