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Error estimations of approximate solutions are given and the highest convergence order can reach four in the sense of the norm of<jats:inline-formula><jats:alternatives><jats:tex-math>$W_{2,0}^{1}$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msubsup><mml:mrow><mml:mi>W<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msubsup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. To overcome the nonlinear condition, we make use of Newton\u2019s method to transform the nonlinear equation into a sequence of linear equations. For the linear equations, a rigorous theory is given for obtaining their<jats:italic>\u03b5<\/jats:italic>-approximate solutions by solving a system of equations or searching the minimum value. Stability analysis is also obtained. Some examples are discussed to illustrate the efficiency of the proposed method.<\/jats:p>","DOI":"10.1007\/s11075-019-00858-9","type":"journal-article","created":{"date-parts":[[2020,1,4]],"date-time":"2020-01-04T11:03:04Z","timestamp":1578135784000},"page":"1123-1153","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A new stable collocation method for solving a class of nonlinear fractional delay differential equations"],"prefix":"10.1007","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1737-9187","authenticated-orcid":false,"given":"Lei","family":"Shi","sequence":"first","affiliation":[]},{"given":"Zhong","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Xiaohua","family":"Ding","sequence":"additional","affiliation":[]},{"given":"Qiang","family":"Ma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,4]]},"reference":[{"key":"858_CR1","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/j.cnsns.2018.04.019","volume":"64","author":"HG Sun","year":"2018","unstructured":"Sun, H.G., Zhang, Y., Baleanu, D., Chen, W., Chen, Y.Q.: A new collection of real world applications of fractional calculus in science and engineering. 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