TWO-STEP REVERSIBLE ENZYMATIC REACTION DYNAMICS MODEL BASED ON FRACTIONAL ORDER OPERATORS WITH GENERALIZED STABILITY AND NUMERICAL RESULTS

Abstract

Chemical kinetics, often known as the kinetics of the reaction, is a discipline related to physical chemistry that looks at the speeds of chemical reactions, experimental settings, as well as the processes and transitional phases of these reactions. This study emphasizes the two-step substrate-enzyme reversible response and chemical kinetics-based modeling and dynamics of enzyme operations. Nonlinear differential equations are converted into fractional-order systems by using the Constant-Proportional Caputo (CPC) operator. We focus on the region that is positively invariant and well-posed in the suggested model. The existence and uniqueness of solutions to nonlinear fractional differential equations with hybrid fractional derivatives are established using Banach's fixed point theorem. Using the Laplace transform method, we investigate the Ulam-Hyers and generalized Ulam-Hyers-Rassias stability for the fractional-order proposed system. We simulate a system of fractional differential equations numerically using the Laplace-Adomian Decomposition Method. Through a variety of figures, the dynamics of reaction against various fractional-orders are depicted. The proposed fractional-order derivative retains the system memory effect, is non-local, and outperforms the integer-order derivative in this regard. The results demonstrate that the suggested approaches are successful in producing superior outcomes.