This paper is devoted to investigating a class of impulsive fractional order differential equations (FODEs) with integral boundary condition. For the proposed paper, we use non-singular type derivative of fractional order which has been introduced by Atangana, Baleanu and Caputo (ABC). The aforesaid type problems have numerous applications in fluid mechanics and hydrodynamics to model various problems of flow phenomenons. We establish some sufficient conditions for the existence and uniqueness of solution to the proposed problem by using classical fixed point results due to Banach and Krasnoselskii. Further, on using tools of the nonlinear analysis, sufficient conditions are developed for Hyers–Ulam (HU) type stability results. A pertinent example is given to justify our results.

本文致力于研究一类具有积分边界条件的脉冲分数阶微分方程 (FODE)。对于拟议的论文，我们使用由 Atangana、Baleanu 和 Caputo (ABC) 引入的分数阶非奇异类型导数。上述类型的问题在流体力学和流体动力学中有大量应用，可以模拟各种流动现象问题。通过使用 Banach 和 Krasnoselskii 的经典不动点结果，我们为所提出问题的解的存在性和唯一性建立了一些充分条件。此外，在使用非线性分析工具时，为 Hyers-Ulam (HU) 型稳定性结果开发了充分条件。给出了一个相关的例子来证明我们的结果。