{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:13:13Z","timestamp":1760058793680,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T00:00:00Z","timestamp":1745539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11901058","2021CFB543"],"award-info":[{"award-number":["11901058","2021CFB543"]}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["11901058","2021CFB543"],"award-info":[{"award-number":["11901058","2021CFB543"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates a class of distributed fractional-order stochastic differential equations driven by fractional Brownian motion with a Hurst parameter 1\/2&lt;H&lt;1. By employing the Picard iteration method, we rigorously prove the existence and uniqueness of solutions with Lipschitz conditions. Furthermore, leveraging the Girsanov transformation argument within the L2 metric framework, we derive quadratic transportation inequalities for the law of the strong solution to the considered equations. These results provide a deeper understanding of the regularity and probabilistic properties of the solutions in this framework.<\/jats:p>","DOI":"10.3390\/sym17050650","type":"journal-article","created":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T10:42:09Z","timestamp":1745577729000},"page":"650","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Probabilistic Analysis of Distributed Fractional-Order Stochastic Systems Driven by Fractional Brownian Motion: Existence, Uniqueness, and Transportation Inequalities"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-6563-4341","authenticated-orcid":false,"given":"Guangyue","family":"Xia","sequence":"first","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113118","DOI":"10.1016\/j.cma.2020.113118","article-title":"A variably distributed-order time-fractional diffusion equation: Analysis and approximation","volume":"367","author":"Yang","year":"2020","journal-title":"Comput. 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