In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann–Liouville fractional derivatives. The standard fixed point theorem like Leray–Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. Also, an example is given to illustrate our theoretical results. The proposed problem is the generalization of third-order ordinary differential equations with classical, initial and anti-periodic boundary conditions.

中文翻译：

---

分数阶边界条件耦合系统的数学分析

在本文中，我们证明了具有分数阶边界条件的分数阶耦合系统的存在性、唯一性和各种 Ulam 稳定性，其中涉及 Riemann-Liouville 分数导数。应用 Leray-Schauder 替代和 Banach 收缩等标准不动点定理来建立存在论和唯一性。此外，我们通过两种方法为上述稳定性建立了充分条件。此外，还给出了一个例子来说明我们的理论结果。提出的问题是具有经典、初始和反周期边界条件的三阶常微分方程的推广。