{"paper":{"title":"A Sobolev Space theory for stochastic partial differential equations with time-fractional derivatives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim","submitted_at":"2016-05-06T01:58:05Z","abstract_excerpt":"In this article we present an $L_p$-theory ($p\\geq 2$) for the time-fractional quasi-linear stochastic partial differential equations (SPDEs) of type $$ \\partial^{\\alpha}_tu=L(\\omega,t,x)u+f(u)+\\partial^{\\beta}_t \\sum_{k=1}^{\\infty}\\int^t_0 ( \\Lambda^k(\\omega,t,x)u+g^k(u))dw^k_t, $$ where $\\alpha\\in (0,2)$, $\\beta <\\alpha+\\frac{1}{2}$, and $\\partial^{\\alpha}_t$ and $\\partial^{\\beta}_t$ denote the Caputo derivative of order $\\alpha$ and $\\beta$ respectively. The processes $w^k_t$, $k\\in \\mathbb{N}=\\{1,2,\\cdots\\}$, are independent one-dimensional Wiener processes defined on a probability space $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01801","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}