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This study introduces a numerical method for the fractional-order predator-prey model with fuzzy initial conditions. The enhanced Euler method provides accurate and efficient solutions for ecological modeling challenges.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Numerical Analysis

Background:

  • Ecological systems are often modeled using predator-prey dynamics.
  • Fractional-order models offer a more nuanced representation of ecological processes.
  • Uncertainty in ecological parameters necessitates robust modeling techniques.

Purpose of the Study:

  • To analyze the fractional-order predator-prey model (FPPM) with uncertainty.
  • To develop and implement a numerical technique for approximate solutions.
  • To address the challenge of fuzzy initial conditions in ecological models.

Main Methods:

  • Implementation of higher-order terms within the fractional Euler method.
  • Application of the numerical technique to the FPPM with fuzzy initial conditions.
  • Validation of the proposed method through a numerical example.

Main Results:

  • The proposed numerical method provides precise approximate solutions for the FPPM.
  • The method effectively handles fuzzy initial conditions arising from uncertain ecological parameters.
  • Numerical results demonstrate the method's authenticity, applicability, and computational ease.

Conclusions:

  • The enhanced fractional Euler method is an efficient and reliable technique for solving the FPPM with uncertainty.
  • The approach offers a valuable tool for ecological modeling where parameters are inherently uncertain.
  • The method's accuracy is validated by comparison with existing techniques like the Homotopy Perturbation Method (HPM).