{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:16:20Z","timestamp":1753881380821,"version":"3.41.2"},"reference-count":36,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T00:00:00Z","timestamp":1542067200000},"content-version":"vor","delay-in-days":316,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009004","name":"Anhui University of Chinese Medicine","doi-asserted-by":"publisher","award":["2018zryb04"],"award-info":[{"award-number":["2018zryb04"]}],"id":[{"id":"10.13039\/501100009004","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The paper concerns the third grade fluid system with the time\u2010fractional derivative of the order <jats:italic>\u03b1<\/jats:italic> \u2208 (0,1). We first establish unique existence criterion of weak solutions in the case that the dimension <jats:italic>n<\/jats:italic> = 3. Then we prove the sufficient condition of optimal pairs.<\/jats:p>","DOI":"10.1155\/2018\/7941012","type":"journal-article","created":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T23:46:00Z","timestamp":1542152760000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Unique Existence of Weak Solution and the Optimal Control for Time\u2010Fractional Third Grade Fluid System"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4427-0235","authenticated-orcid":false,"given":"Guangming","family":"Shao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biao","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6268-8160","authenticated-orcid":false,"given":"Yueying","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,11,13]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"323","article-title":"Stress-deformation relations for isotropic materials","volume":"4","author":"Rivlin R. S.","year":"1955","journal-title":"Journal of Rational Mechanics and Analysis"},{"key":"e_1_2_9_2_2","first-page":"85","article-title":"New equations for the description of the motions of viscous incompressible fluids, and global solvability for their boundary value problems","volume":"102","author":"Ladyzhenskaya O. A.","year":"1967","journal-title":"Trudy Matematicheskogo Instituta Imeni V. A. Steklova"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00250351"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(95)00072-0"},{"key":"e_1_2_9_5_2","first-page":"47","article-title":"Global existence of classical solutions for the equations of third grade fluids","volume":"29","author":"Sequeira A.","year":"1995","journal-title":"Journal of Mathematical and Physical Sciences"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7462(02)00121-X"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2008.03.019"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/20\/5\/003"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2013.08.001"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0252-9602(16)30092-3"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1142\/8934"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1142\/3779"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.07.022"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/num.20420"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.02.011"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.11.025"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2015.04.008"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.03.026"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.07.007"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.03.053"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/8131329"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-008-0068-1"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2970709"},{"key":"e_1_2_9_24_2","first-page":"661","article-title":"On Cauchy problems with CAPuto Hadamard fractional derivatives","volume":"21","author":"Adjabi Y.","year":"2016","journal-title":"Journal of Computational Analysis and Applications"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1594-y"},{"volume-title":"Navier-Stokes Equations","year":"1984","author":"Temam R.","key":"e_1_2_9_26_2"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970050"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-0732-0"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1142\/9069"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(06)80001-0"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/24\/003"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1134\/S0012266110050058"},{"key":"e_1_2_9_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-00891-2"},{"key":"e_1_2_9_34_2","series-title":"Second revised and supplemented edition","volume-title":"Mathematical problems of the dynamics of a viscous incompressible liquid","author":"Ladyzhenskaya O. A.","year":"1970"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/21\/7\/013"},{"volume-title":"Quelques M\u00e9thodes de R\u00e9solution des Probl\u00e8mes aux Limites Non Lin\u00e9aires","year":"1969","author":"Lions J. L.","key":"e_1_2_9_36_2"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2018\/7941012.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2018\/7941012.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2018\/7941012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T22:32:49Z","timestamp":1723156369000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2018\/7941012"}},"subtitle":[],"editor":[{"given":"Viet-Thanh","family":"Pham","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1155\/2018\/7941012"],"URL":"https:\/\/doi.org\/10.1155\/2018\/7941012","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2018,1]]},"assertion":[{"value":"2018-06-10","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-10-22","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"7941012"}}