{"paper":{"title":"A Generalization of the Hopf's Lemma for the 1-D Moving-Boundary Problem for the Fractional Diffusion Equation and its Application to a Fractional Free-Boundary Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sabrina D. Roscani","submitted_at":"2015-02-04T14:44:06Z","abstract_excerpt":"This paper deals with a theoretical mathematical analysis of a one-dimensional-moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order $\\al$ $\\in (0,1)$ is taken in the Caputo's sense. A generalization of the Hopf's lemma is proved, and then this result is used to prove a monotonicity property for the free-boundary when a fractional free-boundary Stefan problem is considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01209","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"}