{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZS7UJ7EVLSNRYZFEL2RIO4IY5G","short_pith_number":"pith:ZS7UJ7EV","schema_version":"1.0","canonical_sha256":"ccbf44fc955c9b1c64a45ea2877118e984fe8bacfca92fef6d121e7bd1df5602","source":{"kind":"arxiv","id":"1707.02314","version":1},"attestation_state":"computed","paper":{"title":"Cauchy-Lipschitz theory for fractional multi-order dynamics -- State-transition matrices, Duhamel formulas and duality theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lo\\\"ic Bourdin","submitted_at":"2017-07-07T18:02:18Z","abstract_excerpt":"The aim of the present paper is to contribute to the development of the study of Cauchy problems involving Riemann-Liouville and Caputo fractional derivatives. Firstly existence-uniqueness results for solutions of non-linear Cauchy problems with vector fractional multi-order are addressed. A qualitative result about the behavior of local but non-global solutions is also provided. Finally the major aim of this paper is to introduce notions of fractional state-transition matrices and to derive fractional versions of the classical Duhamel formula. We also prove duality theorems relying left state"},"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":"1707.02314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-07T18:02:18Z","cross_cats_sorted":[],"title_canon_sha256":"0c3536ea5ff10bc62d66c2c9705c284e18cf937c8676cfd54d663f082f9b0314","abstract_canon_sha256":"e0412c7702dcd059403d09fe0a581ea1c7b038a03e84751066e0b3adfa7692a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:39.556588Z","signature_b64":"kxQQlBOK3Xe11cQP6JshKqQpgDBdYTSkEnj4PbmeCJGaokTNqgOI9VNie1z7PUZiqwY3xEB6e6qfKmjVpKIGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccbf44fc955c9b1c64a45ea2877118e984fe8bacfca92fef6d121e7bd1df5602","last_reissued_at":"2026-05-18T00:40:39.556009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:39.556009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cauchy-Lipschitz theory for fractional multi-order dynamics -- State-transition matrices, Duhamel formulas and duality theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lo\\\"ic Bourdin","submitted_at":"2017-07-07T18:02:18Z","abstract_excerpt":"The aim of the present paper is to contribute to the development of the study of Cauchy problems involving Riemann-Liouville and Caputo fractional derivatives. Firstly existence-uniqueness results for solutions of non-linear Cauchy problems with vector fractional multi-order are addressed. A qualitative result about the behavior of local but non-global solutions is also provided. Finally the major aim of this paper is to introduce notions of fractional state-transition matrices and to derive fractional versions of the classical Duhamel formula. We also prove duality theorems relying left state"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02314","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":"1707.02314","created_at":"2026-05-18T00:40:39.556116+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.02314v1","created_at":"2026-05-18T00:40:39.556116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02314","created_at":"2026-05-18T00:40:39.556116+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZS7UJ7EVLSNR","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZS7UJ7EVLSNRYZFE","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZS7UJ7EV","created_at":"2026-05-18T12:31:59.375834+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/ZS7UJ7EVLSNRYZFEL2RIO4IY5G","json":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G.json","graph_json":"https://pith.science/api/pith-number/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/graph.json","events_json":"https://pith.science/api/pith-number/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/events.json","paper":"https://pith.science/paper/ZS7UJ7EV"},"agent_actions":{"view_html":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G","download_json":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G.json","view_paper":"https://pith.science/paper/ZS7UJ7EV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.02314&json=true","fetch_graph":"https://pith.science/api/pith-number/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/graph.json","fetch_events":"https://pith.science/api/pith-number/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/action/storage_attestation","attest_author":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/action/author_attestation","sign_citation":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/action/citation_signature","submit_replication":"https://pith.science/pith/ZS7UJ7EVLSNRYZFEL2RIO4IY5G/action/replication_record"}},"created_at":"2026-05-18T00:40:39.556116+00:00","updated_at":"2026-05-18T00:40:39.556116+00:00"}