{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:56:40Z","timestamp":1760237800808,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,16]],"date-time":"2022-06-16T00:00:00Z","timestamp":1655337600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"FCT","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020 (CIDMA)"],"award-info":[{"award-number":["UIDB\/04106\/2020 (CIDMA)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel\u2019skii fixed-point theorem we prove, via the Kolmogorov\u2013Riesz criteria, the existence of solutions. The existence results are established in a specific fractional derivative Banach space and they are illustrated by two numerical examples.<\/jats:p>","DOI":"10.3390\/axioms11060295","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T01:48:12Z","timestamp":1655430492000},"page":"295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7619-8584","authenticated-orcid":false,"given":"Djalal","family":"Boucenna","sequence":"first","affiliation":[{"name":"High School of Technological Teaching, Enset, Skikda 21001, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7365-4393","authenticated-orcid":false,"given":"Amar","family":"Chidouh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chadli Bendjedid University, Eltarf 36000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4341","DOI":"10.3934\/mbe.2022201","article-title":"Solution of a dynamical memory effect COVID-19 infection system with leaky vaccination efficacy by non-singular kernel fractional derivatives","volume":"19","author":"Dhar","year":"2022","journal-title":"Math. Biosci. 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