{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T13:23:34Z","timestamp":1725024214233},"reference-count":16,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We utilized the Haar wavelet operational matrix method for fractional order nonlinear oscillation equations and find the solutions of fractional order force-free and forced Duffing-Van der Pol oscillator and higher order fractional Duffing equation on large intervals. The results are compared with the results obtained by the other technique and with exact solution.<\/jats:p>","DOI":"10.1155\/2014\/174819","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T21:03:23Z","timestamp":1405458203000},"page":"1-8","source":"Crossref","is-referenced-by-count":7,"title":["Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations"],"prefix":"10.1155","volume":"2014","author":[{"given":"Umer","family":"Saeed","sequence":"first","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan"}]},{"given":"Mujeeb ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/18.57199"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cta:19970702"},{"key":"3","first-page":"429","volume":"2","year":"2010","journal-title":"International Journal of Computational Science and Mathematics"},{"issue":"11","key":"4","first-page":"11136","volume":"2","year":"2012","journal-title":"Journal of Basic and Applied Scientific Research"},{"key":"5","first-page":"519","volume":"8","year":"1959","journal-title":"Journal of Applied Mathematics and Mechanics"},{"key":"6","year":"1965"},{"key":"7","year":"1981"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2012.06.009"},{"key":"9","doi-asserted-by":"crossref","first-page":"176","DOI":"10.4236\/ajcm.2011.13020","volume":"1","year":"2011","journal-title":"The American Journal of Computational Mathematics"},{"key":"10","first-page":"47","volume":"2","year":"2012","journal-title":"International Journal of Mathematics and Computer Applications Research"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.07.018"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-335-0"},{"issue":"3","key":"15","first-page":"136","volume":"1","year":"2010","journal-title":"Journal of Advanced Research in Mechanical Engineering"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.2000.3050"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.07.003"},{"issue":"1-4","key":"16","first-page":"121","volume":"5","year":"2011","journal-title":"Advanced Studies in Theoretical Physics"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/174819.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/174819.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/174819.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T16:45:56Z","timestamp":1498149956000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2014\/174819\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":16,"alternative-id":["174819","174819"],"URL":"https:\/\/doi.org\/10.1155\/2014\/174819","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}