{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T04:28:53Z","timestamp":1766377733915,"version":"3.41.2"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T00:00:00Z","timestamp":1618876800000},"content-version":"vor","delay-in-days":109,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971475"],"award-info":[{"award-number":["11971475"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schr\u00f6dinger (NLS) equation with Lax integrability is then derived and first\u2010 and second\u2010order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first\u2010 and second\u2010order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer\u2010order derivatives. Besides, the time the second\u2010order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first\u2010 and second\u2010order fractional rogue wave solutions.<\/jats:p>","DOI":"10.1155\/2021\/6669087","type":"journal-article","created":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T01:59:31Z","timestamp":1618970371000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7956-4882","authenticated-orcid":false,"given":"Bo","family":"Xu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4461-5237","authenticated-orcid":false,"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4631-7033","authenticated-orcid":false,"given":"Sheng","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,4,20]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-020-2376-8"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature06402"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1740"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1088\/0253-6102\/54\/5\/31"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.85.026607"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1088\/0256-307X\/28\/11\/110202"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.036604"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2014.02.013"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2016.10.009"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2020.105284"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.106145"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.05.047"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-020-05514-9"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/3206503"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.90.113902"},{"volume-title":"Fractional Differential Equations","year":"1999","author":"Podlubny I.","key":"e_1_2_9_16_2"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.12.051"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.01.029"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1108\/hff-03-2013-0092"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.2298\/tsci1603789z"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2017.09.045"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2018.06.011"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/7952871"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.2298\/tsci180815207z"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.2298\/tsci2004597z"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218348x1850086x"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X19500178"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.2298\/tsci1904131h"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1615\/heattransres.2013005856"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2016.05.010"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/9075823"},{"key":"e_1_2_9_32_2","first-page":"66","article-title":"Time fractional order mZK model and its exact solution in dust plasma","volume":"9","author":"Zhang W. 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