We present a fractional-order epidemic model for childhood diseases with the new fractional derivative approach proposed by Caputo and Fabrizio. By applying the Laplace Adomian decomposition method (LADM), we solve the problem and the solutions are presented as infinite series converging to the solution. We prove the existence, uniqueness, and stability of the solution by using the fixed point theory. Also, we provide some numerical results to illustrate the effectiveness of the new derivative.

中文翻译：

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拉普拉斯阿德曼分解法用Caputo-Fabrizio衍生物模拟儿童流行病

我们用Caputo和Fabrizio提出的新的分数导数方法介绍了儿童疾病的分数阶流行模型。通过应用拉普拉斯阿德曼分解法（LADM），我们解决了该问题，并将解决方案表示为收敛于该解决方案的无限级数。我们使用定点理论证明了该解的存在性，唯一性和稳定性。此外，我们提供了一些数值结果来说明新导数的有效性。