The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using Schaefer’s fixed point theorem and Banach’s contraction principle, the required conditions are developed. Also, different kinds of Ulam stability results are derived by using nonlinear analysis. Providing a pertinent example, we demonstrate our main results.

中文翻译：

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具有脉冲条件的比例滞后隐式分数阶微分方程的非线性积分边值问题的数学分析

当前的研究致力于获得关于具有脉冲和积分边界条件的隐式分数阶微分方程（FODE）非线性问题的存在性和稳定性分析的一些结果。有关问题涉及比例式延迟项。通过使用Schaefer的不动点定理和Banach的收缩原理，开发了所需的条件。此外，通过使用非线性分析可以得出不同类型的Ulam稳定性结果。提供一个相关的例子，我们证明了我们的主要结果。