{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GXMWGPXGSK2HPG6WYWMUDEW45S","short_pith_number":"pith:GXMWGPXG","schema_version":"1.0","canonical_sha256":"35d9633ee692b4779bd6c5994192dcec83ce92da485e4e429b5c780f05b7dd20","source":{"kind":"arxiv","id":"1709.01228","version":1},"attestation_state":"computed","paper":{"title":"On the analysis of mixed-index time fractional differential equation systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fanhai Zeng, Ian W. Turner, Kevin Burrage, Pamela M. Burrage","submitted_at":"2017-09-05T03:55:26Z","abstract_excerpt":"In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace tran"},"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":"1709.01228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-05T03:55:26Z","cross_cats_sorted":[],"title_canon_sha256":"69502fbd8773c376745874604321d8618cfd6fa79177d814705bde25b83b859a","abstract_canon_sha256":"cad228a03f5267a88b31259b0cab3ec0ca7fa8acf0bf8c414ea8ad93ec434aca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:00.628607Z","signature_b64":"b75COaml1IDyx8KnpDjvwEGB+sCmhbTdMBi6/eAMJhg4TEL9kXwyCO3qGXfCcdNt14zkBZO4bSVGoXjhtXRSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35d9633ee692b4779bd6c5994192dcec83ce92da485e4e429b5c780f05b7dd20","last_reissued_at":"2026-05-18T00:36:00.628214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:00.628214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the analysis of mixed-index time fractional differential equation systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fanhai Zeng, Ian W. Turner, Kevin Burrage, Pamela M. Burrage","submitted_at":"2017-09-05T03:55:26Z","abstract_excerpt":"In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01228","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":"1709.01228","created_at":"2026-05-18T00:36:00.628275+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01228v1","created_at":"2026-05-18T00:36:00.628275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01228","created_at":"2026-05-18T00:36:00.628275+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXMWGPXGSK2H","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXMWGPXGSK2HPG6W","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXMWGPXG","created_at":"2026-05-18T12:31:18.294218+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/GXMWGPXGSK2HPG6WYWMUDEW45S","json":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S.json","graph_json":"https://pith.science/api/pith-number/GXMWGPXGSK2HPG6WYWMUDEW45S/graph.json","events_json":"https://pith.science/api/pith-number/GXMWGPXGSK2HPG6WYWMUDEW45S/events.json","paper":"https://pith.science/paper/GXMWGPXG"},"agent_actions":{"view_html":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S","download_json":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S.json","view_paper":"https://pith.science/paper/GXMWGPXG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01228&json=true","fetch_graph":"https://pith.science/api/pith-number/GXMWGPXGSK2HPG6WYWMUDEW45S/graph.json","fetch_events":"https://pith.science/api/pith-number/GXMWGPXGSK2HPG6WYWMUDEW45S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S/action/storage_attestation","attest_author":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S/action/author_attestation","sign_citation":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S/action/citation_signature","submit_replication":"https://pith.science/pith/GXMWGPXGSK2HPG6WYWMUDEW45S/action/replication_record"}},"created_at":"2026-05-18T00:36:00.628275+00:00","updated_at":"2026-05-18T00:36:00.628275+00:00"}