The behavior of any complex dynamic system is a natural result of the interaction between the components of that system. Important examples of these systems are biological models that describe the characteristics of complex interactions between certain organisms in a biological environment. The study of these systems requires the use of precise and advanced computational methods in mathematics. In this paper, we discuss a prey–predator interaction model that includes two competitive predators and one prey with a generalized interaction functional. The primary presumption in the model construction is the competition between two predators on the only prey, which gives a strong implication of the real-world situation. We successfully establish the existence and stability of the equilibria. Further, we investigate the impact of the memory measured by fractional time derivative on the temporal behavior. We test the obtained mathematical results numerically by a proper numerical scheme built using the Caputo fractional-derivative operator and the trapezoidal product-integration rule.

任何复杂的动态系统的行为都是该系统各组件之间相互作用的自然结果。这些系统的重要示例是生物学模型，该模型描述了生物环境中某些生物之间复杂相互作用的特征。对这些系统的研究需要在数学中使用精确而先进的计算方法。在本文中，我们讨论了一个食饵与捕食者的相互作用模型，该模型包括两个竞争性捕食者和一个具有广义相互作用功能的猎物。模型构建的主要假设是两个捕食者在唯一猎物之间的竞争，这给现实世界带来了强烈的暗示。我们成功地建立了平衡的存在性和稳定性。更多，我们研究了分数时间导数测量的记忆对时间行为的影响。我们通过使用Caputo分数微分算子和梯形乘积积分规则构建的适当数值方案，对获得的数学结果进行数值测试。