In this research study, we are concerned with the existence and stability of solutions of a boundary value problem (BVP) of the fractional thermostat control model with ψ-Hilfer fractional operator. We verify the uniqueness criterion via the Banach fixed-point principle and establish the existence by using the Schaefer and Krasnoselskii fixed-point results. Moreover, we apply the arguments related to the nonlinear functional analysis to discuss various types of stability in the format of Ulam. Finally, by several examples we demonstrate applications of the main findings.

中文翻译：

---

关于分数边值问题的定性分析，通过ψ-希尔弗分数算子描述恒温控制模型

在此研究中，我们关注具有ψ- Hilfer分数算子的分数恒温器控制模型的边值问题（BVP）解的存在性和稳定性。我们通过Banach定点原理验证唯一性准则，并通过使用Schaefer和Krasnoselskii定点结果建立存在性。此外，我们使用与非线性泛函分析相关的论据来讨论Ulam格式的各种类型的稳定性。最后，通过几个例子，我们演示了主要发现的应用。