This paper is concerned with the existence and uniqueness, and Ulam–Hyers stabilities of solutions of nonlinear impulsive \(\varphi \)–Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the initial conditions, order of derivative and the functions involved in the equations. The outcomes are acquired in the space of weighted piecewise continuous functions by means of fixed point theorems and the generalized version of Gronwall inequality.

中文翻译：

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脉冲$$ \ varphi $$φ–希尔弗尔分数阶微分方程的分析

本文关注非线性脉冲\（\ varphi \）– Hilfer分数阶微分方程解的存在性和唯一性以及Ulam–Hyers稳定性。此外，我们研究了解对初始条件，导数阶数和方程中涉及的函数的依赖性。通过定点定理和广义Gronwall不等式在加权分段连续函数空间中获取结果。