Mathematical modeling of infectious diseases with non-integer order getting attentions from scientists and researchers day by day. It is obvious that classical models in epidemiology can only be described through a fixed order while models in fractional order derivative are of not fixed order. Having non fixed order the fractional derivative becomes more powerful in modeling real life problems. In the recent era, different novel concepts regarding fractional operators such as the exponential decay and the Mittag–Leffler kernel have been introduced which overcome the limitations of the previous fractional order derivatives. These new operators have been found effective in modeling problems arising in science and engineering. A more recent operator in fractional calculus was introduced that is known as fractal-fractional operator. In this study, we consider this novel approach and apply it to an epidemic model of dengue fever and explore their dynamics. We show some important analysis for the dengue epidemic model in the presence of this new operator. The uniqueness and existence results will be shown. We show the simulation results for the considered model with a novel numerical approach which is not yet considered by anyone for such epidemic model. We obtain results for fractal model when fractional order is one and will have fractional solution when fractal order is one and have when both are present. We show that the fractal-fractional approach is much suitable for an epidemic model rather than fractional operator.

具有非整数顺序的传染病的数学建模日益受到科学家和研究人员的关注。很明显，流行病学中的经典模型只能通过固定的顺序来描述，而分数阶导数的模型则是不固定的顺序。具有非固定阶数的分数导数在模拟现实生活中的问题时变得更加强大。在最近的时代，已经引入了关于分数运算符的不同新概念，例如指数衰减和 Mittag-Leffler 核，它们克服了以前分数阶导数的局限性。已经发现这些新算子在对科学和工程中出现的问题进行建模方面很有效。引入了分数微积分中较新的算子，称为分形分数算子。在这项研究中，我们考虑了这种新颖的方法并将其应用于登革热的流行模型并探索它们的动态。在这个新算子存在的情况下，我们展示了对登革热流行病模型的一些重要分析。将显示唯一性和存在性结果。我们用一种新的数值方法展示了所考虑模型的模拟结果，这种方法尚未被任何人考虑用于这种流行病模型。当分形阶数为 1 时，我们获得分形模型的结果，当分形阶数为 1 时将具有分数解，并且当两者都存在时具有分形解。我们表明分形-分数方法更适合流行病模型而不是分数算子。在这个新算子存在的情况下，我们展示了对登革热流行病模型的一些重要分析。将显示唯一性和存在性结果。我们用一种新的数值方法展示了所考虑模型的模拟结果，这种方法尚未被任何人考虑用于这种流行病模型。当分形阶数为 1 时，我们获得分形模型的结果，当分形阶数为 1 时将具有分数解，并且当两者都存在时具有分形解。我们表明分形-分数方法更适合流行病模型而不是分数算子。在这个新算子存在的情况下，我们展示了对登革热流行病模型的一些重要分析。将显示唯一性和存在性结果。我们用一种新的数值方法展示了所考虑模型的模拟结果，这种方法尚未被任何人考虑用于这种流行病模型。当分形阶数为 1 时，我们获得分形模型的结果，当分形阶数为 1 时将具有分数解，并且当两者都存在时具有分形解。我们表明分形-分数方法更适合流行病模型而不是分数算子。当分形阶数为 1 时，我们获得分形模型的结果，当分形阶数为 1 时将具有分数解，并且当两者都存在时具有分形解。我们表明分形-分数方法更适合流行病模型而不是分数算子。当分形阶数为 1 时，我们获得分形模型的结果，当分形阶数为 1 时将具有分数解，并且当两者都存在时具有分形解。我们表明分形-分数方法更适合流行病模型而不是分数算子。