In this paper, we investigate the existence and uniqueness of a solution for a class of ψ-Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, and Krasnosellskii’s fixed point theorems. Further, applying the techniques of nonlinear functional analysis, we establish various kinds of the Ulam stability results for the analyzed problem, that is, the Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. Finally, we provide some examples to illustrate the applicability of our results.

在本文中，我们研究了一类具有混合非局部条件的ψ -Hilfer隐式分数阶积分-微分方程解的存在性和唯一性。这些论点基于Banach，Schaefer和Krasnosellskii的不动点定理。此外，运用非线性泛函分析技术，我们针对分析的问题建立了各种Ulam稳定性结果，即Ulam-Hyers稳定性，广义Ulam-Hyers稳定性，Ulam-Hyers-Rassias稳定性和广义Ulam-耶尔-拉萨斯稳定。最后，我们提供一些示例来说明我们的结果的适用性。