{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:US3JWXWT22CCOR7V2U26QZSI56","short_pith_number":"pith:US3JWXWT","schema_version":"1.0","canonical_sha256":"a4b69b5ed3d6842747f5d535e86648efb82546b413d45c3de823c6af46d4279a","source":{"kind":"arxiv","id":"1907.05290","version":1},"attestation_state":"computed","paper":{"title":"Growth Equation of the General Fractional Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Anatoly N. Kochubei, Yuri Kondratiev","submitted_at":"2019-07-11T14:59:31Z","abstract_excerpt":"We consider the Cauchy problem $(\\mathbb D_{(k)} u)(t)=\\lambda u(t)$, $u(0)=1$, where $\\mathbb D_{(k)}$ is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory {\\bf 71} (2011), 583--600), $\\lambda >0$. The solution is a generalization of the function $t\\mapsto E_\\alpha (\\lambda t^\\alpha)$ where $0<\\alpha <1$, $E_\\alpha$ is the Mittag-Leffler function. The asymptotics of this solution, as $t\\to \\infty$, is studied."},"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":"1907.05290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-11T14:59:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5790e4cd937fc934fd9ff275700e9261a58e600d3ecfa2769bc6ba6099a1ccfe","abstract_canon_sha256":"6523e5eea553a4ff6493dc8620bf5c69c1a54e08fa8abe478af1b70dbdb91e19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:50.870618Z","signature_b64":"XavpsdwablzuA/i08w94wVTNFLs3Q/BTcx6oV3t7ogPp0ohXhuxQG7Aki9YW7zFgQvdLQaTQWRzhwVJptMnVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4b69b5ed3d6842747f5d535e86648efb82546b413d45c3de823c6af46d4279a","last_reissued_at":"2026-05-17T23:40:50.869992Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:50.869992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth Equation of the General Fractional Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Anatoly N. Kochubei, Yuri Kondratiev","submitted_at":"2019-07-11T14:59:31Z","abstract_excerpt":"We consider the Cauchy problem $(\\mathbb D_{(k)} u)(t)=\\lambda u(t)$, $u(0)=1$, where $\\mathbb D_{(k)}$ is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory {\\bf 71} (2011), 583--600), $\\lambda >0$. The solution is a generalization of the function $t\\mapsto E_\\alpha (\\lambda t^\\alpha)$ where $0<\\alpha <1$, $E_\\alpha$ is the Mittag-Leffler function. The asymptotics of this solution, as $t\\to \\infty$, is studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05290","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":"1907.05290","created_at":"2026-05-17T23:40:50.870070+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05290v1","created_at":"2026-05-17T23:40:50.870070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05290","created_at":"2026-05-17T23:40:50.870070+00:00"},{"alias_kind":"pith_short_12","alias_value":"US3JWXWT22CC","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"US3JWXWT22CCOR7V","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"US3JWXWT","created_at":"2026-05-18T12:33:30.264802+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/US3JWXWT22CCOR7V2U26QZSI56","json":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56.json","graph_json":"https://pith.science/api/pith-number/US3JWXWT22CCOR7V2U26QZSI56/graph.json","events_json":"https://pith.science/api/pith-number/US3JWXWT22CCOR7V2U26QZSI56/events.json","paper":"https://pith.science/paper/US3JWXWT"},"agent_actions":{"view_html":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56","download_json":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56.json","view_paper":"https://pith.science/paper/US3JWXWT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05290&json=true","fetch_graph":"https://pith.science/api/pith-number/US3JWXWT22CCOR7V2U26QZSI56/graph.json","fetch_events":"https://pith.science/api/pith-number/US3JWXWT22CCOR7V2U26QZSI56/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56/action/timestamp_anchor","attest_storage":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56/action/storage_attestation","attest_author":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56/action/author_attestation","sign_citation":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56/action/citation_signature","submit_replication":"https://pith.science/pith/US3JWXWT22CCOR7V2U26QZSI56/action/replication_record"}},"created_at":"2026-05-17T23:40:50.870070+00:00","updated_at":"2026-05-17T23:40:50.870070+00:00"}