{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:R3LE63HLPBWEHSY77ERQGOXAVU","short_pith_number":"pith:R3LE63HL","schema_version":"1.0","canonical_sha256":"8ed64f6ceb786c43cb1ff923033ae0ad1f38b7ab5f2b5a46c790f27f5331d8dd","source":{"kind":"arxiv","id":"1811.02717","version":1},"attestation_state":"computed","paper":{"title":"Leibniz type rule: $\\Psi-$Hilfer fractional derivative","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":"2018-11-07T01:34:37Z","abstract_excerpt":"In this paper, we present the Leibniz rule for the $\\Psi-$Hilfer ($\\Psi-$H) fractional derivative in two versions, the first in relation to $\\Psi-$RL fractional derivative and the second in relation to the $\\Psi-$H fractional derivative. In this sense, we present some particular cases of Leibniz rules and Leibniz type rules from the investigated case."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.02717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-07T01:34:37Z","cross_cats_sorted":[],"title_canon_sha256":"7b80df0235bffb4bf6c78ae098a88c5531b1220355ed9a79cf7183dde1ea2381","abstract_canon_sha256":"e3bbd567cc68abdb9520ec7e9d0b1eccbd170ced7ef8455de7c13fc576d6b626"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:20.960698Z","signature_b64":"PUdEoITv1RZbfw7Ky8plvsLWahHuu5nKKwVhruj42nhRtejEQBoOiqHX0ag9tQ9rUk1RFTDHTeDFtLK6DxtPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ed64f6ceb786c43cb1ff923033ae0ad1f38b7ab5f2b5a46c790f27f5331d8dd","last_reissued_at":"2026-05-18T00:01:20.960184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:20.960184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Leibniz type rule: $\\Psi-$Hilfer fractional derivative","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":"2018-11-07T01:34:37Z","abstract_excerpt":"In this paper, we present the Leibniz rule for the $\\Psi-$Hilfer ($\\Psi-$H) fractional derivative in two versions, the first in relation to $\\Psi-$RL fractional derivative and the second in relation to the $\\Psi-$H fractional derivative. In this sense, we present some particular cases of Leibniz rules and Leibniz type rules from the investigated case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02717","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.02717","created_at":"2026-05-18T00:01:20.960263+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.02717v1","created_at":"2026-05-18T00:01:20.960263+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02717","created_at":"2026-05-18T00:01:20.960263+00:00"},{"alias_kind":"pith_short_12","alias_value":"R3LE63HLPBWE","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"R3LE63HLPBWEHSY7","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"R3LE63HL","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU","json":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU.json","graph_json":"https://pith.science/api/pith-number/R3LE63HLPBWEHSY77ERQGOXAVU/graph.json","events_json":"https://pith.science/api/pith-number/R3LE63HLPBWEHSY77ERQGOXAVU/events.json","paper":"https://pith.science/paper/R3LE63HL"},"agent_actions":{"view_html":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU","download_json":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU.json","view_paper":"https://pith.science/paper/R3LE63HL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.02717&json=true","fetch_graph":"https://pith.science/api/pith-number/R3LE63HLPBWEHSY77ERQGOXAVU/graph.json","fetch_events":"https://pith.science/api/pith-number/R3LE63HLPBWEHSY77ERQGOXAVU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU/action/storage_attestation","attest_author":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU/action/author_attestation","sign_citation":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU/action/citation_signature","submit_replication":"https://pith.science/pith/R3LE63HLPBWEHSY77ERQGOXAVU/action/replication_record"}},"created_at":"2026-05-18T00:01:20.960263+00:00","updated_at":"2026-05-18T00:01:20.960263+00:00"}