ADVANCING LOTKA-VOLTERRA SYSTEM SIMULATION WITH VARIABLE FRACTIONAL ORDER CAPUTO DERIVATIVE FOR ENHANCED DYNAMIC ANALYSIS

This study investigates the application of the Caputo derivative with a variable fractional order to time-dependent models of Ordinary Differential Equations (ODEs), aiming to enhance the simulation accuracy of dynamic systems characterized by complex, nonlinear temporal behaviors. The proposed approach provides a more refined understanding and predictive capability for non-constant real-world phenomena, contributing to the development of advanced scientific and engineering solutions. The research centers on a variable-order Lotka-Volterra predator-prey model, employing the Arzelà-Ascoli and Schaefer fixed point theorems to establish the existence of solutions, and the Banach fixed point theorem to demonstrate their uniqueness. Numerical analyses are conducted to compare the proposed model with its integer-order, fractional-order, and variable-order counterparts, utilizing various time-varying and constant delay functions. The findings validate the efficacy of the proposed method in accurately modeling dynamic systems.