Abstract In this article, we study the existence and uniqueness of solutions of a switched coupled implicit ψ-Hilfer fractional differential system. The existence and uniqueness results are obtained by using fixed point techniques. Further, we investigate different kinds of stability such as Hyers–Ulam stability and Hyers–Ulam–Rassias stability. Finally, an example is provided to illustrate the obtained results.

中文翻译：

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ψ $\boldsymbol{\psi}$-Hilfer 型隐式切换耦合分数阶微分方程的存在性、唯一性和稳定性

摘要 本文研究了切换耦合隐式ψ-Hilfer分数阶微分系统解的存在唯一性。存在性和唯一性结果是通过使用定点技术获得的。此外，我们研究了不同种类的稳定性，例如 Hyers-Ulam 稳定性和 Hyers-Ulam-Rassias 稳定性。最后，提供了一个例子来说明得到的结果。