{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T18:03:28Z","timestamp":1748455408315,"version":"3.40.5"},"reference-count":45,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T00:00:00Z","timestamp":1716854400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Northern Border University","award":["NBU-FFR-2024-1519-03"],"award-info":[{"award-number":["NBU-FFR-2024-1519-03"]}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>In this paper, the existence and uniqueness of solution for a fractional differential model involving well-posed boundary conditions and implicit fractional differential equation is considered. The desired goals are achieved by using Banach contraction principle and Scheafer\u2019s fixed point theorem. To show the results applicability some examples are presented. The basic mathematical concept of well-posed fractional boundary value issues is investigated in this study. It dives into the existence and uniqueness of these difficulties, offering light on the conditions that allow for both practical and singular solutions. This study contributes to a better knowledge of fractional calculus and its applications in a variety of scientific and technical areas, giving significant insights for both scholars and practitioners.<\/jats:p>","DOI":"10.1371\/journal.pone.0303848","type":"journal-article","created":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T17:47:04Z","timestamp":1716918424000},"page":"e0303848","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Existence and uniqueness of well-posed fractional boundary value problem"],"prefix":"10.1371","volume":"19","author":[{"given":"Yuanheng","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5464-0648","authenticated-orcid":true,"given":"Barrira","family":"Jurrat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muddasir","family":"Ejaz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5181-4221","authenticated-orcid":true,"given":"Muhammad","family":"Azeem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1327-2876","authenticated-orcid":true,"given":"M. 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