In this paper, existence, uniqueness, and Hyers-Ulam stability for the solution of second-order fuzzy differential equations (FDEs) are studied. To deal a physical model, it is required to insure whether unique solution of the model exists. The natural transform has the speciality to converge to both Laplace and Sumudu transforms only by changing the variables. Therefore, this method plays the rule of checker on the Laplace and Sumudu transforms. We use natural transform to obtain the solution of the proposed FDEs. As applications of the established results, some nontrivial examples are provided to show the authenticity of the presented work.

中文翻译：

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二阶模糊微分方程解的Hyers-Ulam稳定性和存在判据

本文研究了二阶模糊微分方程(FDE)解的存在性、唯一性和Hyers-Ulam稳定性。处理一个物理模型，需要保证模型的唯一解是否存在。自然变换的特点是仅通过改变变量就可以收敛到拉普拉斯变换和苏木杜变换。因此，该方法对拉普拉斯和苏木杜变换起到了棋盘格规则。我们使用自然变换来获得所提出的 FDE 的解决方案。作为既定结果的应用，提供了一些非平凡的例子来表明所呈现工作的真实性。