{"paper":{"title":"Stabilization of fractional-evolution systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fathi Hassine, Ka\\\"is Ammari, Luc Robbiano","submitted_at":"2019-02-07T10:33:17Z","abstract_excerpt":"This paper is devoted to the analysis of the problem of stabilization of fractional (in time) partial differential equations. We consider the following equation $$ \\partial^{\\alpha,\\eta}_{t} u(t)=\\mathcal{A}u(t)-\\frac{\\eta}{\\Gamma (1-\\alpha)}\\int_{0}^{t}(t-s)^{-\\alpha} \\, e^{-\\eta(t-s)}u(s)\\, ds,\\; t > 0, $$ with the initial data $u(0)=u^{0}$, where $\\mathcal{A}$ is a unbounded operator in Hilbert space and $\\partial_{t}^{\\alpha,\\eta}$ stands for the fractional derivative. We provide two main results concerning the behavior of the solutions when $t\\longrightarrow+\\infty$. We look first to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02558","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"}