{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P6ZJ7OGCAVSJ2MCM2CBEI427LD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5bb0e3bf95cd43c3c9838ee306f228040b43ff04825f0d4b0c6c23938ef1a6df","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-15T19:43:31Z","title_canon_sha256":"195aa2038e20df811f87636eb3ccdf6dc874b09fa401f6ee4c3ba151bc081d9e"},"schema_version":"1.0","source":{"id":"1705.07733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07733","created_at":"2026-05-18T00:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07733v2","created_at":"2026-05-18T00:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07733","created_at":"2026-05-18T00:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"P6ZJ7OGCAVSJ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P6ZJ7OGCAVSJ2MCM","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P6ZJ7OGC","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:31e68fbf3c22ff07bf08ae3e1d44b4d347bc7919e6011b0f9fa1911a1880335e","target":"graph","created_at":"2026-05-18T00:30:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type. As an application, we consider a nonlinear fractional differential equation with an initial condition using this new formulation. We show that this equation is equivalent to a Volterra integral equation and demonstrate the existence and uniqueness of solution to the nonlinear initia","authors_text":"D. S. Oliveira, E. Capelas de Oliveira","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-15T19:43:31Z","title":"Hilfer-Katugampola fractional derivative"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07733","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8caa44d0c438d08ccb66ca5af14418be26eee0cec61520cb145390c94274e63f","target":"record","created_at":"2026-05-18T00:30:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5bb0e3bf95cd43c3c9838ee306f228040b43ff04825f0d4b0c6c23938ef1a6df","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-15T19:43:31Z","title_canon_sha256":"195aa2038e20df811f87636eb3ccdf6dc874b09fa401f6ee4c3ba151bc081d9e"},"schema_version":"1.0","source":{"id":"1705.07733","kind":"arxiv","version":2}},"canonical_sha256":"7fb29fb8c205649d304cd08244735f58f1b88ca27583e2933aca1c394bda3d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb29fb8c205649d304cd08244735f58f1b88ca27583e2933aca1c394bda3d18","first_computed_at":"2026-05-18T00:30:54.893387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:54.893387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HTltmvSFirDWauGMh7e6fUyUVnqiW4teXB1NfO19kUhl261bzwztcBpWIg+Bh7wviZL1D/U1jAuIplN0N9VoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:54.894000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8caa44d0c438d08ccb66ca5af14418be26eee0cec61520cb145390c94274e63f","sha256:31e68fbf3c22ff07bf08ae3e1d44b4d347bc7919e6011b0f9fa1911a1880335e"],"state_sha256":"ed8ddec354f8a2d87fe8498606f0615144e3b04428b3de4563dd002c5eaf873c"}