{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:53:20Z","timestamp":1760237600519,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,8]],"date-time":"2020-06-08T00:00:00Z","timestamp":1591574400000},"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-61-GOV-D-65"],"award-info":[{"award-number":["KMUTNB-61-GOV-D-65"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we establish the existence results for a nonlinear fractional difference equation with delay and impulses. The Banach and Schauder\u2019s fixed point theorems are employed as tools to study the existence of its solutions. We obtain the theorems showing the conditions for existence results. Finally, we provide an example to show the applicability of our results.<\/jats:p>","DOI":"10.3390\/sym12060980","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T06:34:16Z","timestamp":1591684456000},"page":"980","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Nonlinear Fractional Difference Equation with Delay and Impulses"],"prefix":"10.3390","volume":"12","author":[{"given":"Rujira","family":"Ouncharoen","sequence":"first","affiliation":[{"name":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}]},{"given":"Saowaluck","family":"Chasreechai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s11071-013-1065-7","article-title":"Discrete fractional logistic map and its chaos","volume":"75","author":"Wu","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.sigpro.2014.02.022","article-title":"Chaos synchronization of the discrete fractional logistic map","volume":"102","author":"Wu","year":"2014","journal-title":"Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.physa.2016.05.045","article-title":"Chaos synchronization of fractional chaotic maps based on stability results","volume":"460","author":"Wu","year":"2016","journal-title":"Physica A"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Goodrich, C.S., and Peterson, A.C. 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