{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T16:49:53Z","timestamp":1758127793178},"reference-count":0,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,12,28]]},"abstract":"<jats:p>This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced <jats:italic>normalized finite fractional difference <\/jats:italic>is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a <jats:italic>perfect finite fractional difference <\/jats:italic>and, in particular, a powerful <jats:italic>adaptive finite fractional difference<\/jats:italic>, whose excellent performance is illustrated in simulation examples.<\/jats:p>","DOI":"10.2478\/v10006-012-0067-9","type":"journal-article","created":{"date-parts":[[2013,2,13]],"date-time":"2013-02-13T15:21:01Z","timestamp":1360768861000},"page":"907-919","source":"Crossref","is-referenced-by-count":40,"title":["Normalized finite fractional differences: Computational and accuracy breakthroughs"],"prefix":"10.61822","volume":"22","author":[{"given":"Rafa\u0142","family":"Stanis\u0142awski","sequence":"first","affiliation":[]},{"given":"Krzysztof J.","family":"Latawiec","sequence":"additional","affiliation":[]}],"member":"37438","container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/22\/4\/article-p907.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2012.22.issue-4\/v10006-012-0067-9\/v10006-012-0067-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:28:05Z","timestamp":1709202485000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-012-0067-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,28]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.2478\/v10006-012-0067-9","relation":{},"ISSN":["2083-8492","1641-876X"],"issn-type":[{"value":"2083-8492","type":"electronic"},{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2012,12,28]]}}}