{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T07:07:18Z","timestamp":1774595238874,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:00:00Z","timestamp":1649030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-FF-65-36"],"award-info":[{"award-number":["KMUTNB-FF-65-36"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper studies the existence and uniqueness of solutions for a coupled system of Hilfer-type generalized proportional fractional differential equations supplemented with nonlocal asymmetric multipoint boundary conditions. We consider both the scalar and the Banach space case. We apply standard fixed-point theorems to derive the desired results. In the scalar case, we apply Banach\u2019s fixed-point theorem, the Leray\u2013Schauder alternative, and Krasnosel\u2019ski\u012d\u2019s fixed-point theorem. The Banach space case is based on M\u00f6nch\u2019s fixed-point theorem and the technique of the measure of noncompactness. Examples illustrating the main results are presented. Symmetric distance between itself and its derivative can be investigated by replacing the proportional number equal to one half.<\/jats:p>","DOI":"10.3390\/sym14040738","type":"journal-article","created":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T05:50:43Z","timestamp":1649051443000},"page":"738","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["On a Nonlocal Coupled System of Hilfer Generalized Proportional Fractional Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9609-9345","authenticated-orcid":false,"given":"Ayub","family":"Samadi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":false,"given":"Jessada","family":"Tariboon","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Diethelm, K. 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