{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MF3M7QQUM6FPZGWSJWT3EQZZAX","short_pith_number":"pith:MF3M7QQU","schema_version":"1.0","canonical_sha256":"6176cfc214678afc9ad24da7b2433905ede36b63017af03ed1702914fb41d845","source":{"kind":"arxiv","id":"1303.3877","version":1},"attestation_state":"computed","paper":{"title":"Identification of fractional order systems using modulating functions method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Da-Yan Liu (KAUST-CEMSE), LAGIS), LSIS), Olivier Gibaru (INRIA Lille - Nord Europe, Taous-Meriem Laleg-Kirati (KAUST-CEMSE), Wilfrid Perruquetti (INRIA Lille - Nord Europe","submitted_at":"2013-03-15T19:40:46Z","abstract_excerpt":"The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating fun"},"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":"1303.3877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-03-15T19:40:46Z","cross_cats_sorted":[],"title_canon_sha256":"94eef02bccdd68fe93a817d2796fd104385d2449594168bad7883337554db045","abstract_canon_sha256":"495e7e264b53428dd9a54686238faf2f2d435becfd7343f2e5c8139110f4b288"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:42.827679Z","signature_b64":"qELT/j6K+oT5Isx9/5uV9PhJptSGd7QeOtpt3dN/6Ft2ZOo0sMCpJ6g6XXZPdfCuWfHKhHVaEFMWiCX7eOdoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6176cfc214678afc9ad24da7b2433905ede36b63017af03ed1702914fb41d845","last_reissued_at":"2026-05-18T03:30:42.826854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:42.826854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identification of fractional order systems using modulating functions method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Da-Yan Liu (KAUST-CEMSE), LAGIS), LSIS), Olivier Gibaru (INRIA Lille - Nord Europe, Taous-Meriem Laleg-Kirati (KAUST-CEMSE), Wilfrid Perruquetti (INRIA Lille - Nord Europe","submitted_at":"2013-03-15T19:40:46Z","abstract_excerpt":"The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3877","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":"1303.3877","created_at":"2026-05-18T03:30:42.826985+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3877v1","created_at":"2026-05-18T03:30:42.826985+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3877","created_at":"2026-05-18T03:30:42.826985+00:00"},{"alias_kind":"pith_short_12","alias_value":"MF3M7QQUM6FP","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MF3M7QQUM6FPZGWS","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MF3M7QQU","created_at":"2026-05-18T12:27:52.871228+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/MF3M7QQUM6FPZGWSJWT3EQZZAX","json":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX.json","graph_json":"https://pith.science/api/pith-number/MF3M7QQUM6FPZGWSJWT3EQZZAX/graph.json","events_json":"https://pith.science/api/pith-number/MF3M7QQUM6FPZGWSJWT3EQZZAX/events.json","paper":"https://pith.science/paper/MF3M7QQU"},"agent_actions":{"view_html":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX","download_json":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX.json","view_paper":"https://pith.science/paper/MF3M7QQU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3877&json=true","fetch_graph":"https://pith.science/api/pith-number/MF3M7QQUM6FPZGWSJWT3EQZZAX/graph.json","fetch_events":"https://pith.science/api/pith-number/MF3M7QQUM6FPZGWSJWT3EQZZAX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX/action/storage_attestation","attest_author":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX/action/author_attestation","sign_citation":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX/action/citation_signature","submit_replication":"https://pith.science/pith/MF3M7QQUM6FPZGWSJWT3EQZZAX/action/replication_record"}},"created_at":"2026-05-18T03:30:42.826985+00:00","updated_at":"2026-05-18T03:30:42.826985+00:00"}