{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T14:55:01Z","timestamp":1781103301570,"version":"3.54.1"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T00:00:00Z","timestamp":1721088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2024R174"],"award-info":[{"award-number":["PNURSP2024R174"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>After the initiation of Jachymski\u2019s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem.<\/jats:p>","DOI":"10.3390\/axioms13070477","type":"journal-article","created":{"date-parts":[[2024,7,17]],"date-time":"2024-07-17T15:15:19Z","timestamp":1721229319000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2450-3043","authenticated-orcid":false,"given":"Doaa","family":"Filali","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 84428, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3217-8295","authenticated-orcid":false,"given":"Mohammad","family":"Dilshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,16]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. 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