This work is devoted to study a class of fractional integro-differential equations under Caputo-Fabrizo derivative. Thank to Banach's and Krasnoselskii's fixed point theorems, the existence and uniqueness results are established for the considered problem. Further, we also derive some necessary conditions for Hyers-Ulam and generalized Hyers-Ulam type stability analysis to the considered problem. Finally, a pertinent problem is given to illustrate the main results.

中文翻译：

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Caputo-Fabrizio导数下分数阶积分微分方程的研究

这项工作致力于研究Caputo-Fabrizo导数下的一类分数积分-微分方程。由于 Banach 和 Krasnoselskii 的不动点定理，建立了所考虑问题的存在性和唯一性结果。此外，我们还推导出了 Hyers-Ulam 的一些必要条件，并对所考虑的问题进行了广义的 Hyers-Ulam 类型稳定性分析。最后，给出了一个相关问题来说明主要结果。