{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T22:43:27Z","timestamp":1775083407135,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T00:00:00Z","timestamp":1667347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science, Research, and Innovation Fund (NSRF), and Suan Dusit University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation impulsive implicit delay differential equations with boundary conditions. Some findings are established by applying the Banach contraction mapping principle and the Schauder fixed-point theorem. An example is provided that illustrates the theoretical results.<\/jats:p>","DOI":"10.3390\/axioms11110611","type":"journal-article","created":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T03:36:44Z","timestamp":1667360204000},"page":"611","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Existence Solutions for Implicit Fractional Relaxation Differential Equations with Impulsive Delay Boundary Conditions"],"prefix":"10.3390","volume":"11","author":[{"given":"Varaporn","family":"Wattanakejorn","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]},{"given":"Panjaiyan","family":"Karthikeyann","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Vasavi College, Erode 638316, India"}]},{"given":"Sadhasivam","family":"Poornima","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Vasavi College, Erode 638316, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4138-7067","authenticated-orcid":false,"given":"Kulandhaivel","family":"Karthikeyan","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore 641407, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"ref_1","first-page":"19","article-title":"An existence result for fractional integro-differential equations on Banach space","volume":"13","author":"Abdo","year":"2019","journal-title":"J. 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