{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T22:04:04Z","timestamp":1781042644136,"version":"3.54.1"},"reference-count":22,"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\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.<\/jats:p>","DOI":"10.1155\/2013\/598083","type":"journal-article","created":{"date-parts":[[2013,8,21]],"date-time":"2013-08-21T17:02:25Z","timestamp":1377104545000},"page":"1-8","source":"Crossref","is-referenced-by-count":3,"title":["A Collocation Method for Solving Fractional Riccati Differential Equation"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yal\u00e7\u0131n","family":"\u00d6zt\u00fcrk","sequence":"first","affiliation":[{"name":"Ula Ali Ko\u00e7man Vocational Scholl, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, 48000 Mu\u011fla, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ay\u015fe","family":"Anapal\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, 48000 Mu\u011fla, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mustafa","family":"G\u00fclsu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, 48000 Mu\u011fla, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehmet","family":"Sezer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, 45047 Manisa, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"98","reference":[{"issue":"1","key":"1","first-page":"1","volume":"6","year":"2005","journal-title":"Undergraduate Mathematics Journal"},{"key":"2","series-title":"Mathematics in Science and Engineering","volume":"198","year":"1999"},{"key":"3","volume-title":"Nonlinear oscillation with fractional derivative and its applications","year":"1998"},{"issue":"2","key":"4","first-page":"86","volume":"15","year":"1999","journal-title":"Bulletin of Science, Technology & Society"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.01.098"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1115\/1.3167615"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S1007-5704(97)90007-1"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(98)00108-X"},{"key":"10","year":"1990"},{"key":"12","volume-title":"Afterthoughts on interpretation of fractional derivatives and integrals","year":"1998"},{"issue":"3","key":"22","doi-asserted-by":"crossref","first-page":"617","DOI":"10.3390\/mca16030617","volume":"16","year":"2011","journal-title":"Mathematical & Computational Applications"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.06.041"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.008"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.02.009"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1080\/0020739940250501"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1080\/00207160212116"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2006.07.003"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.07.051"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.03.054"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.11.044"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2010.12.044"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.07.102"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/598083.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/598083.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/598083.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,21]],"date-time":"2019-07-21T12:00:30Z","timestamp":1563710430000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/598083\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":22,"alternative-id":["598083","598083"],"URL":"https:\/\/doi.org\/10.1155\/2013\/598083","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}