{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T19:14:19Z","timestamp":1775934859241,"version":"3.50.1"},"reference-count":56,"publisher":"Emerald","issue":"3","license":[{"start":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T00:00:00Z","timestamp":1561939200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["GS"],"published-print":{"date-parts":[[2019,7,1]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(<jats:italic>a<\/jats:italic>, <jats:italic>n<\/jats:italic>) based on the classical GM(1, <jats:italic>n<\/jats:italic>) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>The GM(<jats:italic>\u03b1<\/jats:italic>, <jats:italic>n<\/jats:italic>) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order <jats:italic>a<\/jats:italic> is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(<jats:italic>a<\/jats:italic>, <jats:italic>n<\/jats:italic>) model.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, <jats:italic>n<\/jats:italic>), GM(<jats:italic>a<\/jats:italic>, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(<jats:italic>a<\/jats:italic>, <jats:italic>n<\/jats:italic>) model provides accurate prediction.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Research limitations\/implications<\/jats:title>\n<jats:p>The GM(<jats:italic>a<\/jats:italic>, <jats:italic>n<\/jats:italic>) model is used to predict China\u2019s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(<jats:italic>a<\/jats:italic>, <jats:italic>n<\/jats:italic>) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>It is the first time to investigate the multivariate fractional grey GM(<jats:italic>\u03b1<\/jats:italic>, <jats:italic>n<\/jats:italic>) model, apply it to study the effects of China\u2019s economic growth and urbanization on energy consumption.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/gs-11-2018-0052","type":"journal-article","created":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T03:20:55Z","timestamp":1561000855000},"page":"356-373","source":"Crossref","is-referenced-by-count":52,"title":["Research on a novel fractional GM(<i>\u03b1<\/i>, <i>n<\/i>) model and its 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