In this work, we apply the new idea of fractal fractional operator to the optimal control for Malaria mathematical model, where the derivative is defined in the sense of Caputo and the parameters are modified. In order to minimize the low-risk and high-risk infectious humans, two control variables are introduced. Necessary optimality conditions are derived. Nonstandard finite difference scheme is constructed to simulate the proposed optimal control system. Comparative studies and numerical simulations are presented.

中文翻译：

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一种新型疟疾数学模型的分形分数最优控制；数值方法

在这项工作中，我们将分形分数算子的新思想应用到疟疾数学模型的最优控制中，该模型在Caputo的意义上定义了导数，并修改了参数。为了最小化低风险和高风险的感染者，引入了两个控制变量。得出必要的最优性条件。构建了非标准有限差分方案，以模拟所提出的最优控制系统。介绍了比较研究和数值模拟。