{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:327I2XEOEDXSBLYLJM5H4LD2WV","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":"499f918cc2103962a4edf04c6cde89747b3f15627ad7b05e8c972a8fad2f4132","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T06:59:53Z","title_canon_sha256":"188016429e2da1ba8888d3b85060397d6b7222b830a9ec49eb296c38d1ff5f79"},"schema_version":"1.0","source":{"id":"1907.03088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03088","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03088v1","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03088","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"327I2XEOEDXS","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"327I2XEOEDXSBLYL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"327I2XEO","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:f293238406c312facc6adee324917cdc072e341687fd09cecda343b59f65de40","target":"graph","created_at":"2026-05-17T23:41:16Z","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":"In this article, we consider mild solutions to a class of impulsive fractional evolution equations of order $0<\\alpha<1$. After analyzing analytic results reported in the literature using Mittag-Leffer function, $\\alpha$-resolvent operator theory, we propose a more appropriate new definition of mild solutions for impulsive fractional evolution equations by replacing the impulse term operator $S_\\alpha(t-t_i)$ with $S_\\alpha(t)S_\\alpha^{-1}(t_i)$, where $S_\\alpha^{-1}(t_i)$ denotes the inverse of the fractional solution operator $S_\\alpha(t)$ at $t=t_i, (i=1,2,\\cdots m)$.","authors_text":"Fei Xu, Linxin Shu, Xiao-Bao Shu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T06:59:53Z","title":"A new study on the mild solution for impulsive fractional evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03088","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":"sha256:3a674b3935c15876b69124e0c15ac57b3a1c5c24ff1c2e0f9fb387e9e4cc5665","target":"record","created_at":"2026-05-17T23:41:16Z","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":"499f918cc2103962a4edf04c6cde89747b3f15627ad7b05e8c972a8fad2f4132","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-06T06:59:53Z","title_canon_sha256":"188016429e2da1ba8888d3b85060397d6b7222b830a9ec49eb296c38d1ff5f79"},"schema_version":"1.0","source":{"id":"1907.03088","kind":"arxiv","version":1}},"canonical_sha256":"debe8d5c8e20ef20af0b4b3a7e2c7ab5587846933bffb5fc5cb5e26a80b4781a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"debe8d5c8e20ef20af0b4b3a7e2c7ab5587846933bffb5fc5cb5e26a80b4781a","first_computed_at":"2026-05-17T23:41:16.883241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:16.883241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7yIqF8AnVaLMDUJSDOviMHUXyhj3dzWjvD28gAelpl/u60zaTfoVTjXfb3IBd51OSYD6BtLgz+TkH77NXS7VCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:16.883732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a674b3935c15876b69124e0c15ac57b3a1c5c24ff1c2e0f9fb387e9e4cc5665","sha256:f293238406c312facc6adee324917cdc072e341687fd09cecda343b59f65de40"],"state_sha256":"7c41801d06730de7c09b95a8b54e3f212967859f17901cc766c7c0c5b85fa9d2"}