{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TINRFIGWE5OQV5QMNCKTCROC5A","short_pith_number":"pith:TINRFIGW","schema_version":"1.0","canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","source":{"kind":"arxiv","id":"1601.01476","version":1},"attestation_state":"computed","paper":{"title":"Fractional diffusion-type equations with exponential and logarithmic differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luisa Beghin","submitted_at":"2016-01-07T10:44:01Z","abstract_excerpt":"We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential differential operator expressed in terms of the Riesz-Feller derivative. We prove that this produces a random additional term in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involvi"},"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":"1601.01476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T10:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"ea0a0b85f4a7a0292d45d8c346c7294835a521c83c2706d06906eaf0e7c934de","abstract_canon_sha256":"89c54b790e8b59d10852679a4a24a4fbe24d99a43592440437f49a56f7c2eaf5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:13.541723Z","signature_b64":"hQm3DxdDEaFt11vSqC85LTUaWvxcu+nyGcHNmdnCEQjeoTa8t9n6RcAwPE8MUwcsqBRxnCx0jManOQ2A1m+jDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1b12a0d6275d0af60c68953145c2e82dfb55c89d67f1a6b519ba7cda052754","last_reissued_at":"2026-05-18T01:23:13.541106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:13.541106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional diffusion-type equations with exponential and logarithmic differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luisa Beghin","submitted_at":"2016-01-07T10:44:01Z","abstract_excerpt":"We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential differential operator expressed in terms of the Riesz-Feller derivative. We prove that this produces a random additional term in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involvi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01476","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":"1601.01476","created_at":"2026-05-18T01:23:13.541190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01476v1","created_at":"2026-05-18T01:23:13.541190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01476","created_at":"2026-05-18T01:23:13.541190+00:00"},{"alias_kind":"pith_short_12","alias_value":"TINRFIGWE5OQ","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TINRFIGWE5OQV5QM","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TINRFIGW","created_at":"2026-05-18T12:30:44.179134+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/TINRFIGWE5OQV5QMNCKTCROC5A","json":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A.json","graph_json":"https://pith.science/api/pith-number/TINRFIGWE5OQV5QMNCKTCROC5A/graph.json","events_json":"https://pith.science/api/pith-number/TINRFIGWE5OQV5QMNCKTCROC5A/events.json","paper":"https://pith.science/paper/TINRFIGW"},"agent_actions":{"view_html":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A","download_json":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A.json","view_paper":"https://pith.science/paper/TINRFIGW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01476&json=true","fetch_graph":"https://pith.science/api/pith-number/TINRFIGWE5OQV5QMNCKTCROC5A/graph.json","fetch_events":"https://pith.science/api/pith-number/TINRFIGWE5OQV5QMNCKTCROC5A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/action/storage_attestation","attest_author":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/action/author_attestation","sign_citation":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/action/citation_signature","submit_replication":"https://pith.science/pith/TINRFIGWE5OQV5QMNCKTCROC5A/action/replication_record"}},"created_at":"2026-05-18T01:23:13.541190+00:00","updated_at":"2026-05-18T01:23:13.541190+00:00"}