{"paper":{"title":"Initial boundary value problems for time-fractional evolution equations in Banach spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fikret Golgeleyen, Giuseppe Floridia, Masahiro Yamamoto","submitted_at":"2025-02-10T15:23:32Z","abstract_excerpt":"We consider an initial value problem for time-fractional evolution equation in Banach space $X$: $$ \\pppa (u(t)-a) = Au(t) + F(t), \\quad 0<t<T. \\eqno{(*)} $$ Here $u: (0,T) \\rrrr X$ is an $X$-valued function defined in $(0,T)$, and $a \\in X$ is an initial value. The operator $A$ satisfies a decay condition of resolvent which is common as a generator of analytic semigroup, and in particular, we can treat a case $X=L^p(\\OOO)$ over a bounded domain $\\OOO$ and a uniform elliptic operator $A$ within our framework.\n  First we construct a solution operator $(a, F) \\rrrr u$ by means of $X$-valued Lapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06554","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06554/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"}