Fractional-order modeling and numerical analysis of double intermediate enzymatic reaction model using generalized Euler method

This study investigates the fractional modeling of a double-intermediate enzymatic reaction model using the Caputo derivative. A system of nonlinear fractional differential equations is formulated in a dimensionless form to capture the complex dynamics of intermediate enzymes. The properties of the model are explored using key theorems related to fractional calculus. The generalized Euler method was employed to obtain numerical solutions for various fractional orders, highlighting the memory-dependent behavior of the system. The numerical simulations were consistent with the theoretical expectations, confirming the validity and effectiveness of the proposed method. Various dimensionless parameters were systematically altered, and the corresponding system responses were captured using 2D plots and surface visualizations in MATLAB{}. The simulation results highlighted that variations in these parameters significantly influenced the transient and steady-state dynamics, illustrating their biochemical relevance and the utility of the fractional-order model in capturing such sensitivities.