In this paper, we have extended the model of HIV-1 infection to the fractional mathematical model using Caputo-Fabrizio and Atangana-Baleanu fractional derivative operators. A detailed proof for the existence and the uniqueness of the solution of fractional mathematical model of HIV-1 infection in Atangana-Baleanu sense is presented. Numerical approach is used to find and study the behavior of the solution of the stated model using different derivative operators, and the graphical comparison between the solutions obtained for the Caputo-Fabrizio and the Atangana-Baleanu operator is presented to see which fractional derivative operator is more efficient.

中文翻译：

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不同分数衍生物框架下HIV-1感染分数模型的数值解

在本文中，我们已经使用Caputo-Fabrizio和Atangana-Baleanu分数导数算子将HIV-1感染模型扩展到分数数学模型。给出了关于在Atangana-Baleanu意义上的HIV-1感染分数数学模型的解的存在性和唯一性的详细证明。使用数值方法来查找和研究使用不同导数算子的所述模型的解的行为，并给出了Caputo-Fabrizio和Atangana-Baleanu算子获得的解之间的图形比较，以了解哪个分数导数算子是更高效。