{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:02:05Z","timestamp":1763535725461,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Function of China","award":["11701457"],"award-info":[{"award-number":["11701457"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, by utilizing the resolvent operator theory, the stochastic analysis method and Picard type iterative technique, we first investigate the existence as well as the uniqueness of mild solutions for a class of     \u03b1 \u2208 ( 1 , 2 )    -order Riemann\u2013Liouville fractional stochastic evolution equations of Sobolev type in abstract spaces. Then the symmetrical technique is used to deal with the     \u03b1 \u2208 ( 1 , 2 )    -order Caputo fractional stochastic evolution equations of Sobolev type in abstract spaces. Two examples are given as applications to the obtained results.<\/jats:p>","DOI":"10.3390\/sym12061031","type":"journal-article","created":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T12:19:55Z","timestamp":1592569195000},"page":"1031","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Existence Results of Mild Solutions for the Fractional Stochastic Evolution Equations of Sobolev Type"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9273-1473","authenticated-orcid":false,"given":"He","family":"Yang","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10957-011-9892-5","article-title":"On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay","volume":"152","author":"Wang","year":"2012","journal-title":"J. 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Control"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/1031\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:40:52Z","timestamp":1760175652000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/1031"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,19]]},"references-count":14,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["sym12061031"],"URL":"https:\/\/doi.org\/10.3390\/sym12061031","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,6,19]]}}}