{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:73BRJEXY42NQ3LMH2WMTH7HT7X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9cfd24396122928c10561cd5129007d2fe1fc81fde4dce6d44998eaf85ea6033","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-07T10:33:17Z","title_canon_sha256":"bff16fff96fef2cf13256e0c2e10e53f58ad8df63651d07d6babf41b3fe3599c"},"schema_version":"1.0","source":{"id":"1902.02558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02558","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02558v1","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02558","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"73BRJEXY42NQ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"73BRJEXY42NQ3LMH","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"73BRJEXY","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:439d63309646a314f743dfbac669975ba7a3b3febafbe8d3f9a1ab73ca82965b","target":"graph","created_at":"2026-05-17T23:54:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Fathi Hassine, Ka\\\"is Ammari, Luc Robbiano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-07T10:33:17Z","title":"Stabilization of fractional-evolution systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02558","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:35633bbb53e06a94653032e94f5c8bf66dcd33a37db341ccb7079e0a6035a9dd","target":"record","created_at":"2026-05-17T23:54:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9cfd24396122928c10561cd5129007d2fe1fc81fde4dce6d44998eaf85ea6033","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-07T10:33:17Z","title_canon_sha256":"bff16fff96fef2cf13256e0c2e10e53f58ad8df63651d07d6babf41b3fe3599c"},"schema_version":"1.0","source":{"id":"1902.02558","kind":"arxiv","version":1}},"canonical_sha256":"fec31492f8e69b0dad87d59933fcf3fddc1e1c6dd8624e5d1f48fa81ada2a3d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fec31492f8e69b0dad87d59933fcf3fddc1e1c6dd8624e5d1f48fa81ada2a3d7","first_computed_at":"2026-05-17T23:54:32.864347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:32.864347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WapiWNDkYa4RZmh1eh6THwXEOa73DpQDNu4keJk90rmS8RbclelLHVd4zuobRXR0yV+7EVNj2qGeshNjk87vCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:32.865043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35633bbb53e06a94653032e94f5c8bf66dcd33a37db341ccb7079e0a6035a9dd","sha256:439d63309646a314f743dfbac669975ba7a3b3febafbe8d3f9a1ab73ca82965b"],"state_sha256":"ad994b8d26f99dd1d61aba63da07d5daf4889dd95e92d67007bb10702c169367"}