{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YZGALBXKVSBGXS3CGXCDGA72CU","short_pith_number":"pith:YZGALBXK","schema_version":"1.0","canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","source":{"kind":"arxiv","id":"1810.04209","version":1},"attestation_state":"computed","paper":{"title":"On the Ulam-Hyers stabilities of {\\Psi}-Hilfer fractional differential equation by means of abstract Volterra operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa, Kishor D. Kucche","submitted_at":"2018-10-09T18:43:11Z","abstract_excerpt":"In this paper, we consider the new class of the fractional differential equation involving the abstract Volterra operator in the Banach space and investigate existence, uniqueness and stabilities of Ulam--Hyers on the compact interval $\\Delta=[a,b]$ and on the infinite interval $I=[a,\\infty )$. Our analysis is based on the application of the Banach fixed point theorem and the Gronwall inequality involving generalized $\\Psi$-fractional integral. At last, we performed out an application to elucidate the outcomes got."},"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":"1810.04209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-10-09T18:43:11Z","cross_cats_sorted":[],"title_canon_sha256":"e53f616d5734453e84caa71a2997329026f4f9a599b2465f107e1467c2927e04","abstract_canon_sha256":"bd8527aa3f3e23bacb948dbbc78a64750ee1abaf45a9e72c4ca6bc464a51d5e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:36.231067Z","signature_b64":"Jx4ioK2D7Hpl2c/ju2NAUHXdlua++GWlsRR3vVSA8T9oBfr9qAzV1wQ/31hK8bSI2snIO+plCQGRO50VLFNWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c64c0586eaac826bcb6235c43303fa150f3bcb140df12456875338065f0146c7","last_reissued_at":"2026-05-17T23:45:36.230246Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:36.230246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ulam-Hyers stabilities of {\\Psi}-Hilfer fractional differential equation by means of abstract Volterra operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa, Kishor D. Kucche","submitted_at":"2018-10-09T18:43:11Z","abstract_excerpt":"In this paper, we consider the new class of the fractional differential equation involving the abstract Volterra operator in the Banach space and investigate existence, uniqueness and stabilities of Ulam--Hyers on the compact interval $\\Delta=[a,b]$ and on the infinite interval $I=[a,\\infty )$. Our analysis is based on the application of the Banach fixed point theorem and the Gronwall inequality involving generalized $\\Psi$-fractional integral. At last, we performed out an application to elucidate the outcomes got."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04209","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":"1810.04209","created_at":"2026-05-17T23:45:36.230383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04209v1","created_at":"2026-05-17T23:45:36.230383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04209","created_at":"2026-05-17T23:45:36.230383+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZGALBXKVSBG","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZGALBXKVSBGXS3C","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZGALBXK","created_at":"2026-05-18T12:33:04.347982+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/YZGALBXKVSBGXS3CGXCDGA72CU","json":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU.json","graph_json":"https://pith.science/api/pith-number/YZGALBXKVSBGXS3CGXCDGA72CU/graph.json","events_json":"https://pith.science/api/pith-number/YZGALBXKVSBGXS3CGXCDGA72CU/events.json","paper":"https://pith.science/paper/YZGALBXK"},"agent_actions":{"view_html":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU","download_json":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU.json","view_paper":"https://pith.science/paper/YZGALBXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04209&json=true","fetch_graph":"https://pith.science/api/pith-number/YZGALBXKVSBGXS3CGXCDGA72CU/graph.json","fetch_events":"https://pith.science/api/pith-number/YZGALBXKVSBGXS3CGXCDGA72CU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/action/storage_attestation","attest_author":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/action/author_attestation","sign_citation":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/action/citation_signature","submit_replication":"https://pith.science/pith/YZGALBXKVSBGXS3CGXCDGA72CU/action/replication_record"}},"created_at":"2026-05-17T23:45:36.230383+00:00","updated_at":"2026-05-17T23:45:36.230383+00:00"}