We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

中文翻译：

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使用 Caputo-Fabrizio 导数的 COVID-19 传输的分数微分方程模型。

我们提出了一个带有 Caputo-Fabrizio 导数的 COVID-19 传输的分数阶模型。采用同伦分析法和拉普拉斯变换法相结合的同伦分析变换法（HATM），求解该问题并给出收敛级数的近似解。我们利用不动点理论证明了唯一解的存在和迭代方法的稳定性。我们还提供了模拟病毒传播的数值结果，并将结果与​​ Caputo 导数的结果进行了比较。