{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3Z5UZOSHWV3Q4X2ERUGSOQYCP6","short_pith_number":"pith:3Z5UZOSH","canonical_record":{"source":{"id":"1805.05546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-15T03:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"60478361bf11df5a15719273dc1d0dbded8ae0132e3162fa53c23bd507d7a1fc","abstract_canon_sha256":"5dac9269083e523a01bf7d55bfb5b39093d12a499f94e40aaffd077db1d1a865"},"schema_version":"1.0"},"canonical_sha256":"de7b4cba47b5770e5f448d0d2743027f92deb91cb651ff520163c0390c3d4f12","source":{"kind":"arxiv","id":"1805.05546","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05546","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05546v1","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05546","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"3Z5UZOSHWV3Q","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3Z5UZOSHWV3Q4X2E","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3Z5UZOSH","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3Z5UZOSHWV3Q4X2ERUGSOQYCP6","target":"record","payload":{"canonical_record":{"source":{"id":"1805.05546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-15T03:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"60478361bf11df5a15719273dc1d0dbded8ae0132e3162fa53c23bd507d7a1fc","abstract_canon_sha256":"5dac9269083e523a01bf7d55bfb5b39093d12a499f94e40aaffd077db1d1a865"},"schema_version":"1.0"},"canonical_sha256":"de7b4cba47b5770e5f448d0d2743027f92deb91cb651ff520163c0390c3d4f12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:00.246845Z","signature_b64":"ZACTHVfW00e7tbJ1MkwZWZl8OJ7UUwG6d4Hp1ixhkexKF9cbd3R/ypQw61SFuAwyByt4GWiug3yeP2FcmJiRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de7b4cba47b5770e5f448d0d2743027f92deb91cb651ff520163c0390c3d4f12","last_reissued_at":"2026-05-18T00:16:00.246260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:00.246260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.05546","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ss+lWlB58cKNgxvV3/U8n470JTU4v4A/h57m0gO/PjmvaBZUoU6bZb+7hgIUSPr+SBJrYR6AC2KE1dPDfbLBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:17:21.609996Z"},"content_sha256":"e532968f1b3ae33b689086277424bb319f72af484fc621943f47e598a3ea8930","schema_version":"1.0","event_id":"sha256:e532968f1b3ae33b689086277424bb319f72af484fc621943f47e598a3ea8930"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3Z5UZOSHWV3Q4X2ERUGSOQYCP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the stability of a hyperbolic fractional partial differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa","submitted_at":"2018-05-15T03:16:29Z","abstract_excerpt":"In this paper, by means of the Gronwall inequality, the {\\psi}-Riemann-Liouville fractional partial integral and the {\\psi}-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these results, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solutions of a fractional partial differential equation of hyperbolic type in a Banach space (B, |.|), real or complex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05546","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y68+aYxgSvqUnacaQIrmiujHQxro7s63r7sQSnQzRMQEZS0wai3mhB4YXfAPK45VMnzNfoNGD/wawk1Rtj+LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:17:21.610350Z"},"content_sha256":"a381a9e7374ad3ad4bf834b06019007a4c8da577c35c8d17c3f2e6ea3f725566","schema_version":"1.0","event_id":"sha256:a381a9e7374ad3ad4bf834b06019007a4c8da577c35c8d17c3f2e6ea3f725566"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6/bundle.json","state_url":"https://pith.science/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T23:17:21Z","links":{"resolver":"https://pith.science/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6","bundle":"https://pith.science/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6/bundle.json","state":"https://pith.science/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3Z5UZOSHWV3Q4X2ERUGSOQYCP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3Z5UZOSHWV3Q4X2ERUGSOQYCP6","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":"5dac9269083e523a01bf7d55bfb5b39093d12a499f94e40aaffd077db1d1a865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-15T03:16:29Z","title_canon_sha256":"60478361bf11df5a15719273dc1d0dbded8ae0132e3162fa53c23bd507d7a1fc"},"schema_version":"1.0","source":{"id":"1805.05546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05546","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05546v1","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05546","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"3Z5UZOSHWV3Q","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3Z5UZOSHWV3Q4X2E","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3Z5UZOSH","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:a381a9e7374ad3ad4bf834b06019007a4c8da577c35c8d17c3f2e6ea3f725566","target":"graph","created_at":"2026-05-18T00:16:00Z","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 paper, by means of the Gronwall inequality, the {\\psi}-Riemann-Liouville fractional partial integral and the {\\psi}-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these results, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solutions of a fractional partial differential equation of hyperbolic type in a Banach space (B, |.|), real or complex.","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-15T03:16:29Z","title":"On the stability of a hyperbolic fractional partial differential equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05546","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:e532968f1b3ae33b689086277424bb319f72af484fc621943f47e598a3ea8930","target":"record","created_at":"2026-05-18T00:16:00Z","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":"5dac9269083e523a01bf7d55bfb5b39093d12a499f94e40aaffd077db1d1a865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-15T03:16:29Z","title_canon_sha256":"60478361bf11df5a15719273dc1d0dbded8ae0132e3162fa53c23bd507d7a1fc"},"schema_version":"1.0","source":{"id":"1805.05546","kind":"arxiv","version":1}},"canonical_sha256":"de7b4cba47b5770e5f448d0d2743027f92deb91cb651ff520163c0390c3d4f12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de7b4cba47b5770e5f448d0d2743027f92deb91cb651ff520163c0390c3d4f12","first_computed_at":"2026-05-18T00:16:00.246260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:00.246260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZACTHVfW00e7tbJ1MkwZWZl8OJ7UUwG6d4Hp1ixhkexKF9cbd3R/ypQw61SFuAwyByt4GWiug3yeP2FcmJiRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:00.246845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e532968f1b3ae33b689086277424bb319f72af484fc621943f47e598a3ea8930","sha256:a381a9e7374ad3ad4bf834b06019007a4c8da577c35c8d17c3f2e6ea3f725566"],"state_sha256":"c570609a326a32607115eb3ddd3c4c11f2a0a0fafc149673a61e421a3cf6900b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vl1ypXs7ExQiIAtRd+lXjVEEe4KkwZTBd5qehVYCZKgPG/55VJ0eWggClPsNvzpZx21jZ2GAiLwOqqA5m94xAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:17:21.612275Z","bundle_sha256":"dbc324fca98251dd71e59e382f1e58b0fa0c07ded6e07d2e4b0d16d5b9acef83"}}