{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T06:23:23Z","timestamp":1708496603438},"reference-count":20,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"International Science & Technology Cooperation Program of China","award":["2012DFG61930"],"award-info":[{"award-number":["2012DFG61930"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>A numerical method based on the CAS wavelets is presented for the fractional integrodifferential equations of Bratu type. The CAS wavelets operational matrix of fractional order integration is derived. A truncated CAS wavelets series together with this operational matrix is utilized to reduce the fractional integrodifferential equations to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msup><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>2<\/mml:mn><mml:mi>M<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>. The convergence and error estimation of CAS wavelets are also given. Two examples are included to demonstrate the validity and applicability of the approach.<\/jats:p>","DOI":"10.1155\/2013\/801395","type":"journal-article","created":{"date-parts":[[2013,12,2]],"date-time":"2013-12-02T21:01:51Z","timestamp":1386018111000},"page":"1-7","source":"Crossref","is-referenced-by-count":3,"title":["Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets"],"prefix":"10.1155","volume":"2013","author":[{"given":"Mingxu","family":"Yi","sequence":"first","affiliation":[{"name":"School of Aeronautical Science and Technology, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kangwen","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Aeronautical Science and Technology, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Aeronautical Science and Technology, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lifeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Aeronautical Science and Technology, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.02.107"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2208452"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.01.033"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.12.021"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010474332598"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.07.062"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1137\/090771715"},{"key":"8","series-title":"Mathematics in Science and Engineering","year":"1999"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2007.02.022"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.05.018"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/080730597"},{"key":"12","series-title":"SIAM Monographs on Mathematical Modeling and Computation","year":"1997"},{"key":"13","year":"1962"},{"key":"14","year":"1955"},{"issue":"29\u201332","key":"15","first-page":"1493","volume":"2","year":"2007","journal-title":"International Journal of Contemporary Mathematical Sciences"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.10.021"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.06.059"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.01.050"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.07.017"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.032"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/801395.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/801395.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/801395.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T16:45:07Z","timestamp":1469897107000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/801395\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":20,"alternative-id":["801395","801395"],"URL":"https:\/\/doi.org\/10.1155\/2013\/801395","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}