{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:36:57Z","timestamp":1740141417993,"version":"3.37.3"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T00:00:00Z","timestamp":1683158400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11926331","11601213"],"award-info":[{"award-number":["11926331","11601213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation for Talents of Lingnan Normal University","award":["ZL1612"],"award-info":[{"award-number":["ZL1612"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,6,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper is addressed to the study of the null controllability for integer order integro-differential equations. Unlike the known results for partial differential equations, we need to consider the equation involving a $\\beta -$power of the Laplace operator $(-\\varDelta )^\\beta $ and an integral term. The key point is to construct a suitable state space of the controlled system at the final time. We first discuss a class of hyperbolic integro-differential equation. We prove that the controlled system is null controllable by an Ingham-type estimate. Also, the controllability time is given. On the other hand, by reduction to absurdity, we deduce that the null controllability property fails for a class of parabolic integro-differential equation with $\\beta \\in \\mathbb{N}^+$.<\/jats:p>","DOI":"10.1093\/imamci\/dnad013","type":"journal-article","created":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T21:16:14Z","timestamp":1683234974000},"page":"285-305","source":"Crossref","is-referenced-by-count":0,"title":["On the null controllability of integer order integro-differential equations"],"prefix":"10.1093","volume":"40","author":[{"given":"Xiuxiang","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Lingnan Normal University , 524048 Zhanjiang , China"}]},{"given":"Lijuan","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Lingnan Normal University , 524048 Zhanjiang , China"}]},{"given":"Xin","family":"Wang","sequence":"additional","affiliation":[{"name":"Zhongtai Securities Institute for Financial Studies, Shandong University , 250100 Jinan , China"}]}],"member":"286","published-online":{"date-parts":[[2023,5,4]]},"reference":[{"volume-title":"Families of Exponentials. 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