{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:06Z","timestamp":1740103686125,"version":"3.37.3"},"reference-count":45,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T00:00:00Z","timestamp":1587513600000},"content-version":"unspecified","delay-in-days":0,"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":["11562014","2017MS0108"],"award-info":[{"award-number":["11562014","2017MS0108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of the Inner Mongolia Autonomous Region","award":["11562014","2017MS0108"],"award-info":[{"award-number":["11562014","2017MS0108"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,4,22]]},"abstract":"<jats:p>In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2\u2009+\u20091)-dimensional (2D) cylindrical Kadomtsev\u2013Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev\u2013Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speed<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>\u03bb<\/mml:mi><\/mml:math>, electron number density (through<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>3<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>) and the fractional order<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c9<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.<\/jats:p>","DOI":"10.1155\/2020\/9075823","type":"journal-article","created":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T23:31:03Z","timestamp":1587598263000},"page":"1-16","source":"Crossref","is-referenced-by-count":8,"title":["Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2190-6106","authenticated-orcid":true,"given":"Quansheng","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liguo","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2010.08.038"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4812715"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/6852548"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1063\/1.3657431"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1038\/nature09045"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/53\/7\/001"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1086\/143324"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1080\/14786443109461710"},{"key":"9","first-page":"405","volume":"170","year":"1935","journal-title":"Monthly Notices of the Royal Astronomical Society"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/2806724"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1063\/1.3688877"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5823"},{"key":"13","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/S0375-9601(02)01360-9","volume":"304","year":"2002","journal-title":"Physics Letters A"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1063\/1.3698984"},{"key":"15","first-page":"4057","volume":"372","year":"2018","journal-title":"Physics Letters A"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.08.071"},{"key":"17","first-page":"113701","volume":"14","year":"2017","journal-title":"Physics of Plasmas"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.05.017"},{"key":"19","doi-asserted-by":"crossref","first-page":"210201","DOI":"10.7498\/aps.68.20191045","volume":"68","year":"2019","journal-title":"Acta Physica Sinica"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2018.10.001"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2018.06.011"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.07.018"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.3390\/math7010041"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.10.012"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/2018072"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2017.08.054"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2014.06.023"},{"key":"28","first-page":"225","volume":"5","year":"2017","journal-title":"New Trends in Mathematical Sciences"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1186\/s13661-018-1049-0"},{"key":"30","first-page":"1","volume":"24","year":"2019","journal-title":"Nonlinear Analysis: Modelling and Control"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2020.106285"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2018.10.052"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.10.084"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-018-0289-9"},{"key":"35","first-page":"1","volume":"43","year":"2013","journal-title":"International Journal of Applied Mathematics"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1088\/0253-6102\/58\/5\/02"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.12.094"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2016.05.152"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2018.11.017"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1016\/s0022-247x(02)00180-4"},{"key":"41","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2016.06.012"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1063\/1.2363352"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2006.02.001"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/33\/008"},{"key":"45","doi-asserted-by":"publisher","DOI":"10.1177\/1687814019838357"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/9075823.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/9075823.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/9075823.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T09:36:32Z","timestamp":1615368992000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/9075823\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,22]]},"references-count":45,"alternative-id":["9075823","9075823"],"URL":"https:\/\/doi.org\/10.1155\/2020\/9075823","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,4,22]]}}}