In this paper, we consider the differential equations with right-sided Caputo and left-sided Riemann-Liouville fractional derivatives. Furthermore, the expression of Green’s function is derived, and its properties are investigated. By the fixed-point theorem for both -concave operators and mixed monotone operators, we get the existence and uniqueness of the solution, respectively. As applications, some examples are provided to illustrate our main results.

中文翻译：

---

混合分数阶微分方程唯一非平凡解的存在性。

在本文中，我们考虑带有右侧Caputo和左侧Riemann-Liouville分数阶导数的微分方程。此外，推导了格林函数的表达式，并研究了它的性质。两者的定点定理-凹算子和混合单调算子，我们分别获得了解的存在性和唯一性。作为应用程序，提供了一些示例来说明我们的主要结果。