This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab.

中文翻译：

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具有非奇异核类型导数的捕食与被捕食者耦合系统的存在性理论和近似解

该手稿考虑了非奇异核类型导数下的非线性耦合系统。从存在性理论和近似解析解两个方面研究了所考虑的问题。对于相关的定性理论，使用了一些不动点结果。对于近似解，应用结合Adomian方法的拉普拉斯变换。最后，通过一个有关捕食者－捕食者系统的例子，我们支持我们的结果。使用Matlab给出了一些图形表示。