Ulam stability problems have received considerable attention in the field of differential equations. However, how to effectively build the fuzzy model for Ulam stability problems is less attractive due to varies of differentiabilities requirements. The paper discusses the Ulam stability of fuzzy differential equations in Banach spaces. After introducing the new definitions of differentiabilities for fuzzy number-valued mappings, we give some important properties about these differentiabilities. On these bases, with different differentiabilities and conditions, we prove the Ulam stability of three kinds of fuzzy differential equations. The obtained conclusions generalize the existing results.

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关于模糊微分方程的Ulam稳定性

在微分方程领域，Ulam稳定性问题受到了相当大的关注。但是，由于差异性要求的不同，如何有效地建立针对Ulam稳定性问题的模糊模型的吸引力较小。本文讨论了Banach空间中模糊微分方程的Ulam稳定性。在介绍了模糊数字值映射的微分的新定义之后，我们给出了有关这些微分的一些重要属性。在此基础上，利用不同的微分和条件，证明了三种模糊微分方程的Ulam稳定性。所得结论概括了现有结果。