Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative - Naik, Parvaiz Ahmad; Zehra, Anum; Farman, Muhammad; Shehzad, Aamir; Shahzeen, Sundas; Huang, Zhengxin (Frontiers in Physics, 2024)
Chemical kinetics is a branch of chemistry that investigates the rates of chemical reactions and has applications in cosmology, geology, and physiology. We develop a mathematical model for chemical reactions based on enzyme dynamics and kinetics, which is a two-step substrate-enzyme reversible reaction, and chemical kinetics-based modeling of enzyme functions. The nonlinear differential equations are transformed into fractional-order systems utilizing the constant-proportional Caputo-Fabrizio (CPCF) and constant-proportional Atangana-Baleanu (CPABC) operators. The system of fractional differential equations is simulated using the Laplace-Adomian Decomposition Method at different fractional orders through simulations and numerical results. Both qualitative and quantitative analyses such as boundedness, positivity, unique solution, and feasible concentration for the proposed model with different hybrid operators are provided. The stability analysis of the proposed scheme is also verified by using Picard's stable condition through the fixed point theorem. The system of fractional differential equations is simulated using the Laplace-Adomian Decomposition Method at different fractional orders through simulations and numerical results.