In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives [Formula: see text] and [Formula: see text].

中文翻译：

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分形-分形疟疾传播模型分析

在本文中，控制策略下的疟疾传播 (MT) 模型使用具有指数衰减律和幂律的 Liouville-Caputo 分数阶 (FO) 导数来考虑。对于解决方案，我们使用涉及拉普拉斯变换的迭代技术。我们通过应用不动点理论检查了解决方案的唯一性和存在性 (UE)。此外，还考虑了包括幂律和指数衰减律的分形-分数算子。对于 FO 导数 [公式：参见文本] 和 [公式：参见文本] 的特定值，获得了 MT 模型的数值结果。