Saowaluck ChasreechaiSadhasivam PoornimaPanjaiyan KarthikeyannKulandhaivel KarthikeyanAnoop KumarKirti KaushikThanin Sitthiwirattham2025-03-102025-03-102024AIMS Mathematics2473698810.3934/math.20245632-s2.0-85191697690https://repository.dusit.ac.th//handle/123456789/4486The aim of this paper was to provide systematic approaches to study the existence of results for the system fractional relaxation integro-differential equations. Applied problems require definitions of fractional derivatives, allowing the utilization of physically interpretable boundary conditions. Impulsive conditions serve as basic conditions to study the dynamic processes that are subject to sudden changes in their state. In the process, we converted the given fractional differential equations into an equivalent integral equation. We constructed appropriate mappings and employed the SchaeferÕs fixed-point theorem and the Banach fixed-point theorem to show the existence of a unique solution. We presented an example to show the applicability of our results. © 2024 the Author(s), licensee AIMS Press.All Open Access; Gold Open Accessdelayexistencefixed pointfractional relaxation impulsive integro differential equationsLiouville-Caputo fractional derivativeRiemann-Liouville fractional derivativeuniquenessArticleScopus