{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YZGALBXKVSBGXS3CGXCDGA72CU","short_pith_number":"pith:YZGALBXK","canonical_record":{"source":{"id":"1810.04209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T18:43:11Z","cross_cats_sorted":[],"title_canon_sha256":"e53f616d5734453e84caa71a2997329026f4f9a599b2465f107e1467c2927e04","abstract_canon_sha256":"bd8527aa3f3e23bacb948dbbc78a64750ee1abaf45a9e72c4ca6bc464a51d5e4"},"schema_version":"1.0"},"canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","source":{"kind":"arxiv","id":"1810.04209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04209","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04209v1","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04209","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"pith_short_12","alias_value":"YZGALBXKVSBG","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YZGALBXKVSBGXS3C","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YZGALBXK","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YZGALBXKVSBGXS3CGXCDGA72CU","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T18:43:11Z","cross_cats_sorted":[],"title_canon_sha256":"e53f616d5734453e84caa71a2997329026f4f9a599b2465f107e1467c2927e04","abstract_canon_sha256":"bd8527aa3f3e23bacb948dbbc78a64750ee1abaf45a9e72c4ca6bc464a51d5e4"},"schema_version":"1.0"},"canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:36.231067Z","signature_b64":"Jx4ioK2D7Hpl2c/ju2NAUHXdlua++GWlsRR3vVSA8T9oBfr9qAzV1wQ/31hK8bSI2snIO+plCQGRO50VLFNWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","last_reissued_at":"2026-05-17T23:45:36.230246Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:36.230246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04209","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":"2026-05-17T23:45:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wl50A+FeyGGMSKSu5aMWGdJOn+POhpAhmdZJ7iNwi2F3jKJdYGcjgnSC9Jjk5z6Rb3K0V2VJO4ZsKfyzTYwuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:44:05.157356Z"},"content_sha256":"5b9eced332b689a264122deac1f87928a0b1165655cb9de90d73c3a0bc830487","schema_version":"1.0","event_id":"sha256:5b9eced332b689a264122deac1f87928a0b1165655cb9de90d73c3a0bc830487"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YZGALBXKVSBGXS3CGXCDGA72CU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Ulam-Hyers stabilities of {\\Psi}-Hilfer fractional differential equation by means of abstract Volterra operator","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, Kishor D. Kucche","submitted_at":"2018-10-09T18:43:11Z","abstract_excerpt":"In this paper, we consider the new class of the fractional differential equation involving the abstract Volterra operator in the Banach space and investigate existence, uniqueness and stabilities of Ulam--Hyers on the compact interval $\\Delta=[a,b]$ and on the infinite interval $I=[a,\\infty )$. Our analysis is based on the application of the Banach fixed point theorem and the Gronwall inequality involving generalized $\\Psi$-fractional integral. At last, we performed out an application to elucidate the outcomes got."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04209","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":"2026-05-17T23:45:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmERH5OLxyJCDCCB6UvFFPMtjjAu+eigABdTRTrcB4Lj0eH8v3MM1pDhRqZLjeHzK2OfWTtFzDTkhwaKlgS6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:44:05.157912Z"},"content_sha256":"0032d3eb40e7a749ff9de0753ccd28f57527f85f0503997a081a0f529078e0ca","schema_version":"1.0","event_id":"sha256:0032d3eb40e7a749ff9de0753ccd28f57527f85f0503997a081a0f529078e0ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/bundle.json","state_url":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZGALBXKVSBGXS3CGXCDGA72CU/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":"2026-06-03T14:44:05Z","links":{"resolver":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU","bundle":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/bundle.json","state":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZGALBXKVSBGXS3CGXCDGA72CU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YZGALBXKVSBGXS3CGXCDGA72CU","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":"bd8527aa3f3e23bacb948dbbc78a64750ee1abaf45a9e72c4ca6bc464a51d5e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T18:43:11Z","title_canon_sha256":"e53f616d5734453e84caa71a2997329026f4f9a599b2465f107e1467c2927e04"},"schema_version":"1.0","source":{"id":"1810.04209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04209","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04209v1","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04209","created_at":"2026-05-17T23:45:36Z"},{"alias_kind":"pith_short_12","alias_value":"YZGALBXKVSBG","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YZGALBXKVSBGXS3C","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YZGALBXK","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:0032d3eb40e7a749ff9de0753ccd28f57527f85f0503997a081a0f529078e0ca","target":"graph","created_at":"2026-05-17T23:45:36Z","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, we consider the new class of the fractional differential equation involving the abstract Volterra operator in the Banach space and investigate existence, uniqueness and stabilities of Ulam--Hyers on the compact interval $\\Delta=[a,b]$ and on the infinite interval $I=[a,\\infty )$. Our analysis is based on the application of the Banach fixed point theorem and the Gronwall inequality involving generalized $\\Psi$-fractional integral. At last, we performed out an application to elucidate the outcomes got.","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa, Kishor D. Kucche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T18:43:11Z","title":"On the Ulam-Hyers stabilities of {\\Psi}-Hilfer fractional differential equation by means of abstract Volterra operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04209","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":"sha256:5b9eced332b689a264122deac1f87928a0b1165655cb9de90d73c3a0bc830487","target":"record","created_at":"2026-05-17T23:45:36Z","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":"bd8527aa3f3e23bacb948dbbc78a64750ee1abaf45a9e72c4ca6bc464a51d5e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T18:43:11Z","title_canon_sha256":"e53f616d5734453e84caa71a2997329026f4f9a599b2465f107e1467c2927e04"},"schema_version":"1.0","source":{"id":"1810.04209","kind":"arxiv","version":1}},"canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","first_computed_at":"2026-05-17T23:45:36.230246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:36.230246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jx4ioK2D7Hpl2c/ju2NAUHXdlua++GWlsRR3vVSA8T9oBfr9qAzV1wQ/31hK8bSI2snIO+plCQGRO50VLFNWDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:36.231067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b9eced332b689a264122deac1f87928a0b1165655cb9de90d73c3a0bc830487","sha256:0032d3eb40e7a749ff9de0753ccd28f57527f85f0503997a081a0f529078e0ca"],"state_sha256":"62214265ff7ed6931c06acf39e694a5ce32de583e6ab2decf8bec71b9e32b26d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"no8nAQ8mE3lMu/qWayTI0pAyKggNPRJv70S+Hqe8cRWErHdoNCN4dVSHL7hGyiS8I2myF52UBL7bhRaMG+W6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:44:05.160548Z","bundle_sha256":"5f33ae4c09718253d2af42ffe46ef4f30d6f8cd652716093fe556b4ffdcdb931"}}