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The CTRW model with tempered waiting time measure is the so\u2010called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two\u2010layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods.<\/jats:p>","DOI":"10.1155\/2019\/6071412","type":"journal-article","created":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T23:31:17Z","timestamp":1574724677000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4724-2774","authenticated-orcid":false,"given":"Weiyuan","family":"Ma","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2012-2788","authenticated-orcid":false,"given":"Changpin","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9050-1287","authenticated-orcid":false,"given":"Jingwei","family":"Deng","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,11,25]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2007.11.011"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1142\/3033"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2017.02.034"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.06.059"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/cplx.21622"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0370-1573(00)00070-3"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.08.071"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0895-7177(01)00137-6"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.76.041105"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1029\/2008gl034899"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2014\/09\/p09023"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcomm.2008.08.070030"},{"key":"e_1_2_9_13_2","first-page":"786","article-title":"Self-synchronization of networks with a strong kernel of integrate and fire excitatory neurons","volume":"12","author":"Catsigeras E.","year":"2013","journal-title":"WSEAS Transactions on Mathematics"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2337-1"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2017.2688583"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/tnnls.2015.2425734"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.3390\/e16126286"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.5006194"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.05.045"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2012.07.009"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/19\/7\/070511"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.09.021"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2012.06.050"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.4036807"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2450-1"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-017-1181-7"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.53.4528"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4935069"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1838-7"},{"key":"e_1_2_9_30_2","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1998"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcsi.2009.2024971"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2019026"},{"key":"e_1_2_9_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.04.003"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.08.019"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2014.10.001"},{"key":"e_1_2_9_36_2","doi-asserted-by":"crossref","unstructured":"DadrasS. 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