A qualitative analysis for a nonlinear system of fractional pantograph evolution differential equations (FPEDEs) has been established. Conditions about the solution of the underlying equations have been established in the direction of the existence and uniqueness of the solution. Using results of fixed-point theorems of Krasnoselskii iterations in Banach spaces, we develop the required results. This research work is enriched by establishing the results related to Ulam–Hyers (UH) stability of the problem under consideration via the tools of nonlinear analysis. To validate the reliability of the obtained results, some pertinent examples are given in the manuscript.

中文翻译：

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具有比例时滞的分数阶耦合非线性演化系统

分数阶受电弓演化微分方程 (FPEDEs) 的非线性系统的定性分析已经建立。在解的存在唯一性的方向上建立了关于基础方程解的条件。使用 Banach 空间中 Krasnoselskii 迭代的不动点定理的结果，我们开发了所需的结果。通过使用非线性分析工具建立与所考虑问题的 Ulam-Hyers (UH) 稳定性相关的结果，丰富了这项研究工作。为了验证所得结果的可靠性，手稿中给出了一些相关的例子。