In this paper, a fractional-order predator–prey mathematical model has been developed considering Holling type II functional response. Here, we have investigated the interaction dynamics of prey, middle predator and top predator. We assume that the middle predator consumes only the prey, and the top predator consumes only the middle predator. Here, the logistic growth of prey has been considered. Then, different possible equilibrium points of our proposed system are determined. The stability of our proposed system is investigated around the equilibrium points. Then, some numerical simulations results are presented for better understanding the dynamics of our proposed model. It is found that the fractional-order derivative can improve the stability of our proposed system.

中文翻译：

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分数阶三物种捕食-被捕食模型的稳定性和动力学。

在本文中，考虑了Holling II型功能响应，已经开发了分数阶捕食者－猎物数学模型。在这里，我们研究了食肉动物，中食动物和顶级食肉动物的相互作用动力学。我们假设中间的捕食者仅消耗猎物，而顶部的捕食者仅消耗中间捕食者。在这里，已经考虑了猎物的逻辑增长。然后，确定了我们提出的系统的不同可能的平衡点。在平衡点附近研究了我们提出的系统的稳定性。然后，给出一些数值模拟结果，以更好地理解我们提出的模型的动力学。发现分数阶导数可以提高我们提出的系统的稳定性。