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The fractional Legendre functions together with their fractional differential operational matrices are used to numerically solve the model. In this way, the numerical solutions of vibration displacement of the model are obtained. At the end, the proposed model and algorithm are proved to be effective via analyzing the numerical results and phase position.<\/jats:p>","DOI":"10.1155\/2019\/9234586","type":"journal-article","created":{"date-parts":[[2019,12,6]],"date-time":"2019-12-06T23:37:23Z","timestamp":1575675443000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Numerical Vibration Displacement Solutions of Fractional Drawing Self\u2010Excited Vibration Model Based on Fractional Legendre Functions"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1323-5402","authenticated-orcid":false,"given":"Jiaquan","family":"Xie","sequence":"first","affiliation":[]},{"given":"Yongjiang","family":"Zheng","sequence":"additional","affiliation":[]},{"given":"Zhongkai","family":"Ren","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4989-0529","authenticated-orcid":false,"given":"Tao","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Guangxian","family":"Shen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,12,6]]},"reference":[{"volume-title":"Self-Excited Vibration","year":"2009","author":"Ding W. 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