{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T20:46:13Z","timestamp":1778100373186,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T00:00:00Z","timestamp":1722816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Oradea, Romania"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present paper is dedicated to the examination of maximum and minimum results based on Green\u2019s functions via delta fractional differences for a class of fractional boundary problems. For such a purpose, we built the corresponding Green\u2019s functions based on the falling factorial functions. In addition, using the constructed Green\u2019s function, the positivity of the function and its corresponding delta function are presented. We also verified the occurrence of two distinct functions with the same Green\u2019s function. The maximality and minimality of the Green\u2019s function show a good qualitative agreement. Finally, we considered some special examples to explain the obtained results.<\/jats:p>","DOI":"10.3390\/sym16080991","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T18:21:40Z","timestamp":1722882100000},"page":"991","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Maximum and Minimum Results for the Green\u2019s Functions in Delta Fractional Difference Settings"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq"},{"name":"Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9807-1100","authenticated-orcid":false,"given":"Carlos","family":"Lizama","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica y Ciencia de la Computaci\u00f3n, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 8320000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-7535","authenticated-orcid":false,"given":"Alina Alb","family":"Lupas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0223-4711","authenticated-orcid":false,"given":"Eman","family":"Al-Sarairah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi P.O. Box 127788, United Arab Emirates"},{"name":"Department of Mathematics, Al-Hussein Bin Talal University, P.O. Box 20, Ma\u2019an 71111, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9896-6692","authenticated-orcid":false,"given":"Mohamed","family":"Abdelwahed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,5]]},"reference":[{"key":"ref_1","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Goodrich, C.S., and Peterson, A.C. (2015). 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