In this paper, we study traveling wavefronts in an anomalous diffusion predator–prey model with the modified Leslie–Gower and Holling-type II schemes. We perform a traveling wave analysis to show that the model has heteroclinic trajectories connecting two steady state solutions of the resulting system of fractional partial differential equations and corresponding to traveling wavefronts. This also includes numerical results to show the existence of traveling wavefronts. Furthermore, we obtain the numerical time-dependent solutions in order to show the evolution of wavefronts. We find that wavefronts exist that travel faster in the anomalous subdiffusive regime than in the normal diffusive one. Our results emphasize that the main properties of traveling waves and invasions are altered by anomalous subdiffusion in this model.

中文翻译：

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异常扩散捕食者-猎物模型中的行进波前

在本文中，我们使用修改后的 Leslie-Gower 和 Holling-II 型方案研究了反常扩散捕食者-被捕食者模型中的行波波前。我们进行行波分析，表明该模型具有连接分数偏微分方程所得系统的两个稳态解并对应于行波波前的异宿轨迹。这还包括显示行波波前存在的数值结果。此外，我们获得了与时间相关的数值解，以显示波前的演变。我们发现波前在异常次扩散状态下比在正常扩散状态下传播得更快。我们的结果强调，行波和入侵的主要特性因该模型中的反常次扩散而改变。