{"paper":{"title":"Regularity theory and extension problem for fractional nonlocal parabolic equations and the master equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.PR"],"primary_cat":"math.AP","authors_text":"J. L. Torrea, P. R. Stinga","submitted_at":"2015-11-05T22:58:50Z","abstract_excerpt":"We develop the regularity theory for solutions to space-time nonlocal equations driven by fractional powers of the heat operator $$(\\partial_t-\\Delta)^su(t,x)=f(t,x),\\quad\\hbox{for}~0<s<1.$$ This nonlocal equation of order $s$ in time and $2s$ in space arises in Nonlinear Elasticity, Semipermeable Membranes, Continuous Time Random Walks and Mathematical Biology. It plays for space-time nonlocal equations like the generalized master equation the same role as the fractional Laplacian for nonlocal in space equations. We obtain a pointwise integro-differential formula for $(\\partial_t-\\Delta)^su(t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01945","kind":"arxiv","version":3},"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"}