{"paper":{"title":"Cauchy problem for fractional non-autonomous evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pengyu Chen, Xuping Zhang, Yongxiang Li","submitted_at":"2019-02-27T03:31:05Z","abstract_excerpt":"This paper deals with the following Cauchy problem to nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness $$ \\left\\{\\begin{array}{ll}\n  ^CD^{\\alpha}_tu(t)+A(t)u(t)= f(t,u(t),(Tu)(t), (Su)(t)),\\quad t\\in [0,a], \\\\[12pt]\n  u(0)=A^{-1}(0)u_0\n  \\end{array} \\right. $$ in infinite-dimensional Banach space $E$, where $ ^CD^{\\alpha}_t$ is the standard Caputo's fractional time derivative of order $0<\\alpha\\leq 1$, $A(t)$ is a family of closed linear operators defined on a dense domain $D(A)$ in Banach space $E$ into $E$ such that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10321","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"}