Analysis of variable-order fractional enzyme kinetics model with time delay.

Area of Science:

• Biochemistry and Chemical Kinetics
• Mathematical Modeling in Biological Systems

Background:

• Enzyme kinetics is crucial for optimizing biotechnological and pharmaceutical processes.
• Traditional models may not fully capture memory effects or nonlocal behaviors in enzymatic reactions.
• Past system states can significantly influence reaction dynamics.

Purpose of the Study:

• To develop a refined enzyme kinetics model incorporating variable-order Caputo fractional derivatives and time delays.
• To accurately capture memory effects and nonlocal behaviors in enzymatic reactions.
• To improve the characterization of biological catalytic processes.

Main Methods:

• Utilizing variable-order Caputo fractional derivatives to model enzyme kinetics.
• Incorporating constant time delays to represent memory effects.
• Applying fixed-point theory to establish the existence and uniqueness of solutions.
• Analyzing model stability using Ulam-Hyers and generalized Ulam-Hyers concepts.
• Employing a robust numerical approach to explore model dynamics.

Main Results:

• The existence and uniqueness of solutions for the proposed fractional model were established.
• The stability of the model was rigorously analyzed.
• Numerical simulations demonstrated the significance of the variable-order Caputo fractional derivative with time delay.
• The model effectively captures intricate dynamics influenced by memory and nonlocal properties.

Conclusions:

• The proposed variable-order fractional enzyme kinetics model with time delay offers a more precise characterization of biological catalytic processes.
• This advanced model refines conventional enzyme kinetics by accounting for memory effects.
• The findings have implications for optimizing processes in biotechnology, pharmaceuticals, and food industries.