# Three-species predator-prey model with respect to Caputo and Caputo-Fabrizio fractional operators

## TL;DR

This paper introduces a new numerical method for analyzing three-species predator-prey models using Caputo and Caputo-Fabrizio fractional derivatives, highlighting the impact of operator type and order on system stability.

## Contribution

It develops an enhanced Adams-Bashforth based numerical scheme for Caputo-Fabrizio operators and compares stability conditions with Caputo derivatives.

## Key findings

- Operator type and order significantly affect system stability.
- The new numerical method improves stability analysis.
- Dynamics vary with fractional operator choice.

## Abstract

We study distributed lag effects in three-dimensional Lotka-Volterra systems by applying the concept of fractional calculus. We derive a new numerical method that provides enhanced stability for the Caputo-Fabrizio operator based on Adams-Bashforth method, considering non-singular kernel in the definition of Caputo-Fabrizio operator. We investigate the stability conditions of this system with comparisons to the Caputo fractional derivative. Numerical results show that the type of differential operators and the value of orders significantly influence the stability of the numerical solution, and dynamics of the Lotka-Volterra system.