{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:39:38Z","timestamp":1753886378150,"version":"3.41.2"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T00:00:00Z","timestamp":1719014400000},"content-version":"vor","delay-in-days":173,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004054","name":"King Abdulaziz University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>This paper aims to introduce a novel variation of almost Hardy\u2013Rogers (<jats:italic>\u03c8<\/jats:italic>, <jats:italic>\u03d5<\/jats:italic>)\u2010type multivalued contraction and <jats:italic>\u03d1<\/jats:italic>\u2010type contraction mappings. The main focus is on proving new fixed point (FP) results in <jats:italic>M<\/jats:italic><jats:sub><jats:italic>\u2118<\/jats:italic><\/jats:sub>\u2010metric space (<jats:italic>M<\/jats:italic><jats:sub><jats:italic>\u2118<\/jats:italic><\/jats:sub>\u2010MS). Additionally, several consequences are derived from our main findings. To elucidate the recency of our outcomes, various examples are provided. Finally, we utilize the obtained results to scrutinize the existence of solutions for nonlinear fourth\u2010order differential equations (NFODEs).<\/jats:p>","DOI":"10.1155\/2024\/6620429","type":"journal-article","created":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T08:33:54Z","timestamp":1719045234000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Solvability of Fourth\u2010Order Differential Equations under Almost Hardy\u2013Rogers (<i>\u03c8<\/i>, <i>\u03d5<\/i>)\u2010Type Multivalued Contractions in <i>M<\/i><sub><i>\u2118<\/i><\/sub>\u2010Metric Space"],"prefix":"10.1155","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7625-3436","authenticated-orcid":false,"given":"Mustafa","family":"Mudhesh","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-328X","authenticated-orcid":false,"given":"Muhammad","family":"Arshad","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6578-7908","authenticated-orcid":false,"given":"Amer Hassan","family":"Albargi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3580-1855","authenticated-orcid":false,"given":"Eskandar","family":"Ameer","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2024,6,22]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-3-1-133-181"},{"key":"e_1_2_12_2_2","first-page":"71","article-title":"Some remarks on fixed points","volume":"60","author":"Kannan R.","year":"1960","journal-title":"Bulletin of the Calcutta Mathematical Society"},{"key":"e_1_2_12_3_2","first-page":"1","article-title":"Kannan\u2019s fixed point theorem","volume":"4","author":"Reich S.","year":"1971","journal-title":"Bollettino Dell\u2019unione Matematica Italiana"},{"key":"e_1_2_12_4_2","first-page":"727","article-title":"Fixed-point theorems","volume":"25","author":"Chatterjea S. 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