{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:54Z","timestamp":1740134514272,"version":"3.37.3"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T00:00:00Z","timestamp":1530489600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2018,7,2]]},"abstract":"<jats:p>Contraction theory regards the convergence between two arbitrary system trajectories. In this article we have introduced partial contraction theory as an extension of contraction theory to analyze coupled identical fractional order systems. It can, also, be applied to study the synchronization phenomenon in networks of various structures and with arbitrary number of systems. We have used partial contraction theory to derive exact and global results on synchronization and antisynchronization of fractional order systems.<\/jats:p>","DOI":"10.1155\/2018\/9414835","type":"journal-article","created":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T20:52:52Z","timestamp":1530564772000},"page":"1-9","source":"Crossref","is-referenced-by-count":0,"title":["Partial Contraction Analysis of Coupled Fractional Order Systems"],"prefix":"10.1155","volume":"2018","author":[{"given":"Ahmad","family":"Ruzitalab","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9711-6936","authenticated-orcid":true,"given":"Mohammad Hadi","family":"Farahi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran"}]},{"given":"Gholamhossien","family":"Erjaee","sequence":"additional","affiliation":[{"name":"School of Physical Sciences, University of California, Irvine, USA"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755743"},{"issue":"14","key":"2","doi-asserted-by":"crossref","first-page":"2350","DOI":"10.1016\/j.physleta.2007.11.065","volume":"372","year":"2008","journal-title":"Physics Letters A"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.06.006"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.05.054"},{"year":"2017","key":"6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1140\/epjnbp13"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1038\/35065745"},{"year":"2006","series-title":"Springer Communications and Control Engineering","key":"9"},{"issue":"5-6","key":"10","first-page":"636","volume":"56","year":"2011","journal-title":"Romanian Journal of Physics"},{"key":"11","first-page":"963","volume-title":"Stability results for fractional differential equations with applications to control processing","volume":"2","year":"1996"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.4173\/mic.2010.3.2"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)00019-3"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690460317"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.2009619"},{"issue":"3","key":"18","first-page":"329","volume":"13","year":"2010","journal-title":"Fractional Calculus and Applied Analysis"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1177\/1077546313481839"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1109\/81.989172"},{"year":"2007","key":"21"},{"issue":"1","key":"22","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1140\/epjst\/e2011-01379-1","volume":"193","year":"2011","journal-title":"The European Physical Journal-Special Topics"},{"year":"2015","key":"23"},{"year":"2010","key":"24"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-004-0527-x"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.07.051"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2015.09.012"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2018\/9414835.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2018\/9414835.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2018\/9414835.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T20:52:54Z","timestamp":1530564774000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2018\/9414835\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,2]]},"references-count":24,"alternative-id":["9414835","9414835"],"URL":"https:\/\/doi.org\/10.1155\/2018\/9414835","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2018,7,2]]}}}