{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UIIR5S63QYRCXVLEUJTFNGZPPF","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":"dffe8188724c793c0c2eb1b8851ad3ee80a95ae406bc359070a00850f00ee292","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-28T17:00:49Z","title_canon_sha256":"70fac22fe169e930667fa0fa278b8b829fcc79664e9674b400154c693d9d4288"},"schema_version":"1.0","source":{"id":"1504.07568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07568","created_at":"2026-05-18T02:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07568v1","created_at":"2026-05-18T02:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07568","created_at":"2026-05-18T02:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"UIIR5S63QYRC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UIIR5S63QYRCXVLE","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UIIR5S63","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:b4c0e517282a6f16532f4e7c03d74a61fc34a9746304dee6c714eba92539c335","target":"graph","created_at":"2026-05-18T02:17:34Z","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":"We consider fractional relaxation and fractional oscillation equations involving Erdelyi-Kober integrals. In terms of Riemann-Liouville integrals, the equations we analyze can be understood as equations with time-varying coefficients. Replacing Riemann-Liouville integrals with Erdelyi-Kober-type integrals in certain fractional oscillation models, we obtain some more general integro-differential equations. The corresponding Cauchy-type problems can be solved numerically, and, in some cases analytically, in terms of Saigo-Kilbas Mittag-Leffler functions. The numerical results are obtained by a t","authors_text":"M. Concezzi, R. Garra, R. Spigler","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-28T17:00:49Z","title":"Fractional relaxation and fractional oscillation models involving Erdelyi-Kober integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07568","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":"sha256:70784cdbcb69e26c2c094bdea7d8628504f61abb76d47ddd44ef109975deaf3c","target":"record","created_at":"2026-05-18T02:17:34Z","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":"dffe8188724c793c0c2eb1b8851ad3ee80a95ae406bc359070a00850f00ee292","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-28T17:00:49Z","title_canon_sha256":"70fac22fe169e930667fa0fa278b8b829fcc79664e9674b400154c693d9d4288"},"schema_version":"1.0","source":{"id":"1504.07568","kind":"arxiv","version":1}},"canonical_sha256":"a2111ecbdb86222bd564a266569b2f7962a3e32609adc46f010a73a6301e2336","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2111ecbdb86222bd564a266569b2f7962a3e32609adc46f010a73a6301e2336","first_computed_at":"2026-05-18T02:17:34.400291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:34.400291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5sap4p9bUbHLTIyux0D48yCFp6XZImAkaSWMRAmsJQ8GSYjNF4vVL1JxMAEHHGilgmt4Z2r5mO2yWoy/iFuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:34.401090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70784cdbcb69e26c2c094bdea7d8628504f61abb76d47ddd44ef109975deaf3c","sha256:b4c0e517282a6f16532f4e7c03d74a61fc34a9746304dee6c714eba92539c335"],"state_sha256":"311a7efda4e28ef05a5384339abd2dc72bf379181d02d3a8aadb3733ca5b2268"}