{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:46:54Z","timestamp":1753886814932,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,22]],"date-time":"2012-04-22T00:00:00Z","timestamp":1335052800000},"content-version":"vor","delay-in-days":112,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>A new method for solving nonlinear Volterra\u2010Fredholm\u2010Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.<\/jats:p>","DOI":"10.1155\/2012\/714973","type":"journal-article","created":{"date-parts":[[2012,4,22]],"date-time":"2012-04-22T21:02:16Z","timestamp":1335128536000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A New Direct Method for Solving Nonlinear Volterra\u2010Fredholm\u2010Hammerstein Integral Equations via Optimal Control Problem"],"prefix":"10.1155","volume":"2012","author":[{"given":"M. A.","family":"El-Ameen","sequence":"first","affiliation":[]},{"given":"M.","family":"El-Kady","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,22]]},"reference":[{"key":"e_1_2_6_1_2","first-page":"288","article-title":"Volterra-fredholm integral equation with carlman kernel in position and time","volume":"4","author":"Khamis A. K.","year":"2009","journal-title":"Journal of Engineering and Applied Sciences"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(89)90138-X"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(91)90041-R"},{"key":"e_1_2_6_4_2","first-page":"122","article-title":"Approximate solutions of nonlinear Fredholm integral equations","volume":"5","author":"El-Ameen M. A.","year":"2011","journal-title":"Applied Mathematics & Information Sciences"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970852"},{"key":"e_1_2_6_6_2","first-page":"33","article-title":"The numerical analysis of Adomian\u2019s decomposition method for nonlinear Volterra integral and integro-differential equations","volume":"8","author":"Maleknejad K.","journal-title":"International Journal of Engineering Science"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1142\/3444"},{"volume-title":"Integral Equations","year":"1982","author":"Tricomi F. G.","key":"e_1_2_6_8_2"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.01.018"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543234"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569609"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.02.042"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.02.041"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(00)00165-X"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2005.02.035"},{"key":"e_1_2_6_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2007.02.007"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.11.181"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/714973.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/714973.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/714973","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:53:09Z","timestamp":1718088789000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/714973"}},"subtitle":[],"editor":[{"given":"Shuyu","family":"Sun","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/714973"],"URL":"https:\/\/doi.org\/10.1155\/2012\/714973","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-12-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-28","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"714973"}}