Abstract In this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

中文翻译：

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一类新的脉冲隐式序列分数微分方程的分析

摘要 在本文中，我们研究了具有非瞬时脉冲和多点边界条件的隐式序列分数阶微分方程。文章根据广义的迪亚兹马戈利斯不动点定理，综合阐述了四种不同类型的乌拉姆稳定性。此外，还构造了一些充分条件来观察所提出模型的解的存在性和唯一性。所提出的模型包含整数阶和分数阶导数。因此，指数函数出现在所提出模型的解中，这将引导研究人员使用众所周知的整数阶微分方程方法研究分数阶微分方程。最后，提供了几个例子来说明我们主要结果的适用性。