On coupled nonlinear evolution system of fractional order with a proportional delay.

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. [ABSTRACT FROM AUTHOR]