The purpose of this work is to analyze the dynamics of dengue fever in newly introduced operator known as fractal-fractional Atangana-Baleanu. Initially, we formulate a new dengue model with hospitalization class of notified infected cases and present the model basic results. Stability results for the model are shown when ${\mathcal{R}}_0<1$. We estimate the parameters for the model considering the infected cases occur in East Java Indonesia for the year 2018. We estimated that the basic reproduction number for this model is approximately equal to ${\mathcal{R}}_0\approx 1.8463$. We show the application of the fractal-fractional Atangana-Baleanu operator to the dengue model and present its numerical solution with a new method. We show the fractal-fractional model versus model fitting for different values of fractal and fractional orders and suggest that the fractal-fractional model provides better fitting to the infected cases of dengue infection. Some numerical results for different orders of fractal and fractional are shown for the validity and the applicability of the newly introduced operator.

这项工作的目的是分析新近引进的名为“ Afractana-Baleanu”分形分数的算子中的登革热动态。最初，我们根据已通报感染病例的住院类别来制定新的登革热模型，并介绍该模型的基本结果。在以下情况下显示模型的稳定性结果${\mathcal{[R}}_0<\mathrm{1个}$。考虑到受感染的病例在东爪哇印度尼西亚，发生在2018年，我们估计该模型的参数。我们估计该模型的基本繁殖数量大约等于${\mathcal{[R}}_0\approx 1.8463$。我们展示了分数维-分数分数Atangana-Baleanu算子在登革热模型中的应用，并提出了一种采用新方法的数值解。我们展示了分形和分数阶模型对比模型对不同分形和分数阶值的拟合，并提出了分形-分数模型可以更好地拟合登革热感染病例。对于新引入的算子的有效性和适用性，显示了不同分数阶和分数阶的一些数值结果。