{"paper":{"title":"Discrete and continuous fractional persistence problems - the positivity property and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anna Szafra\\'nska, Jacky Cresson","submitted_at":"2016-04-07T20:32:20Z","abstract_excerpt":"In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical ($\\alpha=1$) differential equation in the fractional case (here using fractional Caputo's derivatives) and the numerical scheme which are associated (here with discrete Gr\\\"unwald-Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability of these points. We formulate explicit conditions under which a fractional system preserves positivity. We deduce also sufficient conditions to ensure order pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02169","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"}