{"paper":{"title":"Mixed linear fractional boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Ifan Johnston, Vassili Kolokoltsov","submitted_at":"2019-08-08T16:36:32Z","abstract_excerpt":"In this article we obtain two-sided estimates for the Greens function of fractional boundary value problems on $\\mathbb R_+ \\times \\mathbb R_+ \\times \\mathbb R^d$ of the form \\[(-{}_{t_1}D^\\beta_{0+*} - {}_{t_2}D^\\gamma_{0+*})u(t_1, t_2, x) = L_{x}u(t_1, t_2, x),\\] with some prescribed boundary functions on the boundaries $\\{0\\} \\times \\mathbb R_+ \\times \\mathbb R^d$ and $\\mathbb R_+ \\times\\{0\\}\\times \\mathbb R^d$. The operators ${}_{t_1}D^\\beta$ and ${}_{t_1}D^\\gamma$ are Caputo fractional derivatives of order $\\beta, \\gamma \\in (0, 1)$ and $L_{x}$ is the generator of a diffusion semigroup: $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03158","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03158/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}