{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WA5XFLSWVSAJTQJN4L4UN3J5U5","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":"3513decfe74b49e69c407a2eb1fe3d89faa0449c05a7c263ddb5490791e55db5","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-09T15:30:07Z","title_canon_sha256":"1828fa1a83f0ee8312939d427d5f6e512d09d00f5ff9aa9c90678be804f2f707"},"schema_version":"1.0","source":{"id":"1004.1577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1577","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1577v1","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1577","created_at":"2026-05-18T00:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"WA5XFLSWVSAJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WA5XFLSWVSAJTQJN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WA5XFLSW","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:7adc83adfb1f7d5bc2cc6a372a5f748a0a9d6ded1874bc98fbdae55a9e3bcea2","target":"graph","created_at":"2026-05-18T00:56:38Z","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 a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by  \\citet{nigmatullin}, and  \\citet{zaslavsky} in  $\\mathbb R^d$  for modeling some physical phenomena.\n The fractional derivative models time delays in a diffusion process. We will give a  survey of the recent results on the fractional Cauchy problem and its generalizations on bounded domains $D\\subset \\rd$ obtained in \\citet{m-n-v-aop, mnv-2}. We also study the solutions of fractional Cauchy problem where the first time derivative is replaced with a","authors_text":"Erkan Nane","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-09T15:30:07Z","title":"Fractional Cauchy problems on bounded domains: survey of recent results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1577","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":"sha256:4ef99e40ac9fed67a50bd7c26cce65806548268ab610ed2309aa7c21e562b62d","target":"record","created_at":"2026-05-18T00:56:38Z","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":"3513decfe74b49e69c407a2eb1fe3d89faa0449c05a7c263ddb5490791e55db5","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-09T15:30:07Z","title_canon_sha256":"1828fa1a83f0ee8312939d427d5f6e512d09d00f5ff9aa9c90678be804f2f707"},"schema_version":"1.0","source":{"id":"1004.1577","kind":"arxiv","version":1}},"canonical_sha256":"b03b72ae56ac8099c12de2f946ed3da764fefbfb87e5ea35371f00fce8bc74e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b03b72ae56ac8099c12de2f946ed3da764fefbfb87e5ea35371f00fce8bc74e8","first_computed_at":"2026-05-18T00:56:38.520377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:38.520377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9r53a4YlWmHZuRVaBlWH2oQUC1mySPhVR3GVTcF0gWm98DaMwU4O1t7zs1G/7PEvzyDwEKNkXdiicpZyRncvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:38.520993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ef99e40ac9fed67a50bd7c26cce65806548268ab610ed2309aa7c21e562b62d","sha256:7adc83adfb1f7d5bc2cc6a372a5f748a0a9d6ded1874bc98fbdae55a9e3bcea2"],"state_sha256":"2515e066aed52f743b1357ca58b958ea41e920d911a9b8115cafa609a8cdca40"}