{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QWRE4DBKEWWHF3H6YDA44WJLQI","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":"65d60830adc95390655e60b4865d4abf0e5446cb0e73e70c6f403207349fbed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-03T14:00:39Z","title_canon_sha256":"9b1dcd4ffb32d817d26dc481c26c5f05242623cb00cee3929caeb95e830590d9"},"schema_version":"1.0","source":{"id":"1801.04995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04995","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04995v2","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04995","created_at":"2026-05-18T00:24:46Z"},{"alias_kind":"pith_short_12","alias_value":"QWRE4DBKEWWH","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QWRE4DBKEWWHF3H6","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QWRE4DBK","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:1dc2fea05e2ad5a085d6a7c1ca3d35cf6c0ed963846e973c373f1186ba5caf23","target":"graph","created_at":"2026-05-18T00:24:46Z","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":"The main objective of this article is to present $\\nu$-fractional derivative $\\mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $\\nu$-fractional derivative satisfies various properties of order calculus such as chain rule, product rule, Rolle's and mean-value theorems for $\\mu$-differentiable function and its extension. Moreover, we define the generalized form of inverse property and the fundamental theorem of calculus and the mean-value theorem for integrals. Also, we establish a relationship with fractional integral ","authors_text":"A. Ghaffar, Azeema, G. Rahman, K. S. Nisar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-03T14:00:39Z","title":"Extended Mittag-Leffler Function and truncated $\\nu$-fractional derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04995","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":"sha256:7ec4800df63cd5200dfd5194f210563f06e3ab0059ebb1e3f8e82c7d6b465105","target":"record","created_at":"2026-05-18T00:24:46Z","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":"65d60830adc95390655e60b4865d4abf0e5446cb0e73e70c6f403207349fbed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-03T14:00:39Z","title_canon_sha256":"9b1dcd4ffb32d817d26dc481c26c5f05242623cb00cee3929caeb95e830590d9"},"schema_version":"1.0","source":{"id":"1801.04995","kind":"arxiv","version":2}},"canonical_sha256":"85a24e0c2a25ac72ecfec0c1ce592b823947806ecca6855128cbf891ca6ebb6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85a24e0c2a25ac72ecfec0c1ce592b823947806ecca6855128cbf891ca6ebb6b","first_computed_at":"2026-05-18T00:24:46.908430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:46.908430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkNYB2QB+DCWkTP5bWsft+EXFFhlRPCZu8K8SJ8zFApMgOEBZwGoCjBjJNMXbMYui0YR9MXxr1MWRLlZ1cQ0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:46.909130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ec4800df63cd5200dfd5194f210563f06e3ab0059ebb1e3f8e82c7d6b465105","sha256:1dc2fea05e2ad5a085d6a7c1ca3d35cf6c0ed963846e973c373f1186ba5caf23"],"state_sha256":"de110bd8dd59c2660cb6c24936af8937ce45fea6a8ab4c5d26f46271a269c816"}