{"paper":{"title":"Space-time fractional stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Erkan Nane, Jebessa B. Mijena","submitted_at":"2014-09-25T18:57:03Z","abstract_excerpt":"We consider non-linear time-fractional stochastic heat type equation $$\\partial^\\beta_tu_t(x)=-\\nu(-\\Delta)^{\\alpha/2} u_t(x)+I^{1-\\beta}_t[\\sigma(u)\\stackrel{\\cdot}{W}(t,x)]$$ in $(d+1)$ dimensions, where $\\nu>0, \\beta\\in (0,1)$, $\\alpha\\in (0,2]$ and $d<\\min\\{2,\\beta^{-1}\\}\\a$, $\\partial^\\beta_t$ is the Caputo fractional derivative, $-(-\\Delta)^{\\alpha/2} $ is the generator of an isotropic stable process, $I^{1-\\beta}_t$ is the fractional integral operator, $\\stackrel{\\cdot}{W}(t,x)$ is space-time white noise, and $\\sigma:\\RR{R}\\to\\RR{R}$ is Lipschitz continuous.\n  Time fractional stochastic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7366","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"}