The aim of this paper is to study the stability of generalized Liouville–Caputo fractional differential equations in Hyers–Ulam sense. We show that three types of the generalized linear Liouville–Caputo fractional differential equations are Hyers–Ulam stable by a ρ -Laplace transform method. We establish existence and uniqueness of solutions to the Cauchy problem for the corresponding nonlinear equations with the help of fixed point theorems.

中文翻译：

---

Hyers-Ulam 稳定性和广义 Liouville-Caputo 分数阶微分方程解的存在性

本文的目的是研究广义 Liouville-Caputo 分数阶微分方程在 Hyers-Ulam 意义上的稳定性。我们通过 ρ -拉普拉斯变换方法证明了三种广义线性 Liouville-Caputo 分数阶微分方程是 Hyers-Ulam 稳定的。借助不动点定理，我们建立了对应非线性方程的柯西问题解的存在唯一性。