In this paper, our main objective is to develop the conditions that assure the existence of solution to a system of boundary value problems (BVPs) of sequential hybrid fractional differential equations (SHFDEs). The problem is considered under the nonlinear boundary conditions. Nonlinear functions involved in the considered system of SHFDEs are continuous and satisfy the growth conditions. We convert the system of SHFDEs to the system of fixed points problem by using the technique of the topological degree theory also called prior estimate method. We establish sufficient conditions that guarantee the existence and uniqueness of positive solution to the system under consideration. Moreover, suitable results are also developed for the Hyers–Ulam stability analysis for the solution of the considered problem. An example is also included to reveal our main result.

中文翻译：

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使用先验估计方法研究序列混合分数微分方程

在本文中，我们的主要目标是开发确保存在求解序列混合分数阶微分方程 (SHFDE) 的边值问题 (BVP) 系统的条件。该问题是在非线性边界条件下考虑的。所考虑的 SHFDE 系统中涉及的非线性函数是连续的并且满足增长条件。我们利用拓扑度理论的技术，也称为先验估计方法，将SHFDEs系统转换为不动点系统。我们建立充分条件来保证所考虑系统的正解的存在性和唯一性。此外，还为解决所考虑问题的 Hyers-Ulam 稳定性分析开发了合适​​的结果。