{"paper":{"title":"Semi-dynamical systems generated by autonomous Caputo fractional differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Peter E. Kloeden, T.S. Doan","submitted_at":"2019-05-22T14:17:06Z","abstract_excerpt":"An autonomous Caputo fractional differential equation of order $\\alpha\\in(0,1)$ in $\\mathbb{R}^d$ whose vector field satisfies a global Lipschitz condition is shown to generate a semi-dynamical system in the function space $\\mathfrak{C}$ of continuous functions $f:\\R^+\\rightarrow \\R^d$ with the topology uniform convergence on compact subsets.\n  This contrasts with a recent result of Cong \\& Tuan \\cite{cong}, which showed that such equations do not, in general, generate a dynamical system on the space $\\mathbb{R}^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09159","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"}