Predator–prey models appear in various fields of bio-mathematics used for the analysis of interactions of biological systems. Due to the complexities of the physical context for the real-world problems of food chain dynamics, introducing new models compatible with experimental results stays ongoing research. Many models have been proposed and analyzed for these systems in recent years. In this paper, we propose a new fractional-order predator–prey model with negative feedback on both species with memory-dependent effects, which increases the compatibility level of the model. Then we present a novel Laguerre spectral numerical simulation for the proposed model by introducing Laguerre modal basis functions with collocation and Galerkin techniques. We then transfer the nonlinear model into a system of algebraic equations, which is solved by efficient numerical solvers. Finally, we provide some test problems to show the efficiency of the proposed model and the computational method.

捕食者－被捕食者模型出现在用于分析生物系统相互作用的生物数学的各个领域。由于实际环境中食物链动力学问题的复杂性，引入与实验结果兼容的新模型仍在进行中。近年来，针对这些系统已经提出并分析了许多模型。在本文中，我们提出了一个新的分数阶捕食者－食饵模型，该模型对两种物种都具有负反馈，具有记忆依赖效应，从而提高了模型的兼容性。然后，通过结合配置和Galerkin技术引入Laguerre模态基函数，为提出的模型提供了新颖的Laguerre谱数值模拟。然后，我们将非线性模型转换为代数方程组，这是由有效的数值求解器解决的。最后，我们提供了一些测试问题，以证明所提出模型和计算方法的有效性。