{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ER3CN42ORDDITTNSA23SAXHQKU","short_pith_number":"pith:ER3CN42O","schema_version":"1.0","canonical_sha256":"247626f34e88c689cdb206b7205cf0551b9db2c2ac7b95a608806f395f814e51","source":{"kind":"arxiv","id":"1704.04254","version":3},"attestation_state":"computed","paper":{"title":"Numerical Approximation of Space-time Fractional Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andrea Bonito, Joseph E. Pasciak, Wenyu Lei","submitted_at":"2017-04-13T19:01:27Z","abstract_excerpt":"In this paper, we develop a numerical scheme for the space-time fractional parabolic equation, i.e., an equation involving a fractional time derivative and a fractional spatial operator. Both the initial value problem and the non-homogeneous forcing problem (with zero initial data) are considered. The solution operator $E(t)$ for the initial value problem can be written as a Dunford-Taylor integral involving the Mittag-Leffler function $e_{\\alpha,1}$ and the resolvent of the underlying (non-fractional) spatial operator over an appropriate integration path in the complex plane. Here $\\alpha$ de"},"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":"1704.04254","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-13T19:01:27Z","cross_cats_sorted":[],"title_canon_sha256":"96189e7ea9bdd2e5bf1dfcc906bee331968d295ec25bf3304d3c6eb550b9dca4","abstract_canon_sha256":"9118a9b6c052efffa62dcc1b4ce0df25478d350af99ecf1649dac2d13cebe4b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:54.472155Z","signature_b64":"gS8VLGdcMwLN13xUQ0o1s2mTcG9LHTQ3eEkVfDQZnTxgjb5I2gad7cL6UOez3wmt+c/10IQe+mzNde5cqWr/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"247626f34e88c689cdb206b7205cf0551b9db2c2ac7b95a608806f395f814e51","last_reissued_at":"2026-05-18T00:37:54.471747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:54.471747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical Approximation of Space-time Fractional Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andrea Bonito, Joseph E. Pasciak, Wenyu Lei","submitted_at":"2017-04-13T19:01:27Z","abstract_excerpt":"In this paper, we develop a numerical scheme for the space-time fractional parabolic equation, i.e., an equation involving a fractional time derivative and a fractional spatial operator. Both the initial value problem and the non-homogeneous forcing problem (with zero initial data) are considered. The solution operator $E(t)$ for the initial value problem can be written as a Dunford-Taylor integral involving the Mittag-Leffler function $e_{\\alpha,1}$ and the resolvent of the underlying (non-fractional) spatial operator over an appropriate integration path in the complex plane. Here $\\alpha$ de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04254","kind":"arxiv","version":3},"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":"1704.04254","created_at":"2026-05-18T00:37:54.471811+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.04254v3","created_at":"2026-05-18T00:37:54.471811+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04254","created_at":"2026-05-18T00:37:54.471811+00:00"},{"alias_kind":"pith_short_12","alias_value":"ER3CN42ORDDI","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"ER3CN42ORDDITTNS","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"ER3CN42O","created_at":"2026-05-18T12:31:12.930513+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/ER3CN42ORDDITTNSA23SAXHQKU","json":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU.json","graph_json":"https://pith.science/api/pith-number/ER3CN42ORDDITTNSA23SAXHQKU/graph.json","events_json":"https://pith.science/api/pith-number/ER3CN42ORDDITTNSA23SAXHQKU/events.json","paper":"https://pith.science/paper/ER3CN42O"},"agent_actions":{"view_html":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU","download_json":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU.json","view_paper":"https://pith.science/paper/ER3CN42O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.04254&json=true","fetch_graph":"https://pith.science/api/pith-number/ER3CN42ORDDITTNSA23SAXHQKU/graph.json","fetch_events":"https://pith.science/api/pith-number/ER3CN42ORDDITTNSA23SAXHQKU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU/action/storage_attestation","attest_author":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU/action/author_attestation","sign_citation":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU/action/citation_signature","submit_replication":"https://pith.science/pith/ER3CN42ORDDITTNSA23SAXHQKU/action/replication_record"}},"created_at":"2026-05-18T00:37:54.471811+00:00","updated_at":"2026-05-18T00:37:54.471811+00:00"}