{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T10:12:42Z","timestamp":1760609562828,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T00:00:00Z","timestamp":1697673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The existence of at least three weak solutions to a discrete fractional boundary value problem containing a p-Laplacian operator and subject to perturbations is proved using variational methods. Some applications of the main results are presented. The results obtained generalize some recent results on both discrete fractional boundary value problems and p-Laplacian boundary value problems. Examples illustrating the results are given.<\/jats:p>","DOI":"10.3390\/axioms12100991","type":"journal-article","created":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T11:46:26Z","timestamp":1697715986000},"page":"991","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Existence of Multiple Weak Solutions to a Discrete Fractional Boundary Value Problem"],"prefix":"10.3390","volume":"12","author":[{"given":"Shahin","family":"Moradi","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416-13534, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ghasem A.","family":"Afrouzi","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416-13534, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8149-4633","authenticated-orcid":false,"given":"John R.","family":"Graef","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Diethelm, K. 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