In this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

中文翻译：

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多项混合多阶分数边值问题及其Ulam-Hyers型稳定性分析的研究

在这项研究工作中，研究了一个新提出的多项混合多阶分数边值问题。假设的混合分数阶微分方程涉及黎曼-刘维尔分数阶导数和多阶类型积分的存在性结果是使用 Dhage 技术推导出来的，该技术处理三个算子的组合。之后，检查其 Ulam-Hyers 类型的稳定性分析和相关推广。最后提供了一些说明性的数值例子来说明和验证我们获得的结果。