In this article, the Bielecki metric on the space $𝒞([a,b])$ is used to analyze the different types of stability results of nonlinear fractional integral equation with delay in its corresponding fractional boundary value problems. Sufficient conditions are obtained to prove stability results for fractional nonlinear Volterra and Fredholm integral equations with delay, given by Ulam, Hyer, and Rassias. Further, those stability results are extended to the fractional integral equations where the domain of integration is an unbounded interval. Two numerical examples are provided to assert the obtained stability results.

中文翻译：

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使用 Bielecki 度量的一些非线性分数积分方程的 Hyers-Ulam-Rassias 稳定性结果

在本文中，空间上的 Bielecki 度量$𝒞([\mathrm{一种},b])$用于分析非线性分数阶积分方程在其对应分数边值问题中的不同类型时滞稳定性结果。获得了足够的条件来证明 Ulam、Hyer 和 Rassias 给出的具有延迟的分数非线性 Volterra 和 Fredholm 积分方程的稳定性结果。此外，这些稳定性结果扩展到分数积分方程，其中积分域是无界区间。提供了两个数值示例来断言所获得的稳定性结果。