| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0243 |
| Advancing Lotka-Volterra System Simulation with Variable Fractional Order Caputo Derivative for Enhanced Dynamic Analysis |
| Parvaiz Ahmad Naik,S Naveen,V Parthiban,Sania Qureshi,Marwan Alquran,Mehmet Senol |
| Keywords:Caputo Chaotic behavior Existence and Uniqueness Fixed point theory Arzela- Ascoli and Schaefer Numerical analysis. |
| Abstract: |
| The study utilizes the Caputo derivative with variable fractional order for time-varying
models of Ordinary Differential Equations (ODEs), enhancing the simulation of dynamic
systems and their complex, nonlinear temporal behaviors. This methodology significantly
improves the understanding and prediction of non-constant real-world phenomena, leading
to advanced scientific and engineering solutions. Focusing on a variable-order Lokta-Volterra
predator-prey model, the research employs Arzela-Ascoli and Schaefer’s fixed point theorems
to establish solution existence, and the Banach fixed point theorem for uniqueness. Numerical
comparisons are drawn between the proposed model and its integer, fractional, and variableorder
versions, using various time-varying and constant delay functions. The results confirm
the effectiveness of this approach in modeling dynamic systems. |
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