We aim in this paper to study the effect of harvesting on predator–prey interaction in the case of prey herd behavior using a fractional-order model. Herd behavior has a crucial role in the surviving of species where it gave them the sufficient protection for the prey that perform it. The objective of using the fractional-order model is to model the memory effect measured by the order of the fractional derivative on the mutual interactions. Further, we aim to seek the effect of inner competition among the predators (also super-predators) on the evolution of the three species. For the mathematical results, we will show the local stability of the equilibria, and show the effect of memory rate and harvesting of the asymptotic behavior of the solution. Moreover, an efficient numerical scheme has been used to provide the numerical illustrations for our study.

我们在本文中的目的是研究在使用分数阶模型的猎物群体行为的情况下收获对捕食者 - 猎物相互作用的影响。群体行为在物种的生存中起着至关重要的作用，它为它们提供了足够的保护来保护执行它的猎物。使用分数阶模型的目的是模拟分数阶导数对相互作用的记忆效应。此外，我们的目标是寻求捕食者（也是超级捕食者）之间的内部竞争对这三个物种进化的影响。对于数学结果，我们将展示平衡的局部稳定性，并展示记忆率和收获对解的渐近行为的影响。而且，