In this study, we aim to comprehensively investigate a drinking model connected to immigration in terms of Atangana-Baleanu derivative in Caputo type. To do this, we firstly extend the model describing drinking model by changing the derivative with time fractional derivative having Mittag-Leffler kernel. The existence and uniqueness of the drinking model solutions together with the stability analysis is shown by the help of Banach fixed point theorem. The special solution of the model is investigated using the Sumudu transformation and then, we present some numerical simulations for the different fractional orders to emphasize the effectiveness of the used derivative.

中文翻译：

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非奇异核导数移民效应下酗酒模型的系统响应

在这项研究中，我们旨在全面调查与卡普托类型的 Atangana-Baleanu 衍生物相关的与移民相关的饮酒模型。为此，我们首先通过使用具有 Mittag-Leffler 核的时间分数导数改变导数来扩展描述饮酒模型的模型。Banach不动点定理证明了饮酒模型解的存在唯一性以及稳定性分析。使用Sumudu变换研究了模型的特解，然后，我们提出了不同分数阶的一些数值模拟，以强调所用导数的有效性。