{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QWRE4DBKEWWHF3H6YDA44WJLQI","short_pith_number":"pith:QWRE4DBK","schema_version":"1.0","canonical_sha256":"85a24e0c2a25ac72ecfec0c1ce592b823947806ecca6855128cbf891ca6ebb6b","source":{"kind":"arxiv","id":"1801.04995","version":2},"attestation_state":"computed","paper":{"title":"Extended Mittag-Leffler Function and truncated $\\nu$-fractional derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Ghaffar, Azeema, G. Rahman, K. S. Nisar","submitted_at":"2018-01-03T14:00:39Z","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 "},"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":"1801.04995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-03T14:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"9b1dcd4ffb32d817d26dc481c26c5f05242623cb00cee3929caeb95e830590d9","abstract_canon_sha256":"65d60830adc95390655e60b4865d4abf0e5446cb0e73e70c6f403207349fbed1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:46.909130Z","signature_b64":"tkNYB2QB+DCWkTP5bWsft+EXFFhlRPCZu8K8SJ8zFApMgOEBZwGoCjBjJNMXbMYui0YR9MXxr1MWRLlZ1cQ0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85a24e0c2a25ac72ecfec0c1ce592b823947806ecca6855128cbf891ca6ebb6b","last_reissued_at":"2026-05-18T00:24:46.908430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:46.908430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extended Mittag-Leffler Function and truncated $\\nu$-fractional derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Ghaffar, Azeema, G. Rahman, K. S. Nisar","submitted_at":"2018-01-03T14:00:39Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04995","kind":"arxiv","version":2},"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":"1801.04995","created_at":"2026-05-18T00:24:46.908545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04995v2","created_at":"2026-05-18T00:24:46.908545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04995","created_at":"2026-05-18T00:24:46.908545+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWRE4DBKEWWH","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWRE4DBKEWWHF3H6","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWRE4DBK","created_at":"2026-05-18T12:32:50.500415+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/QWRE4DBKEWWHF3H6YDA44WJLQI","json":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI.json","graph_json":"https://pith.science/api/pith-number/QWRE4DBKEWWHF3H6YDA44WJLQI/graph.json","events_json":"https://pith.science/api/pith-number/QWRE4DBKEWWHF3H6YDA44WJLQI/events.json","paper":"https://pith.science/paper/QWRE4DBK"},"agent_actions":{"view_html":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI","download_json":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI.json","view_paper":"https://pith.science/paper/QWRE4DBK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04995&json=true","fetch_graph":"https://pith.science/api/pith-number/QWRE4DBKEWWHF3H6YDA44WJLQI/graph.json","fetch_events":"https://pith.science/api/pith-number/QWRE4DBKEWWHF3H6YDA44WJLQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI/action/storage_attestation","attest_author":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI/action/author_attestation","sign_citation":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI/action/citation_signature","submit_replication":"https://pith.science/pith/QWRE4DBKEWWHF3H6YDA44WJLQI/action/replication_record"}},"created_at":"2026-05-18T00:24:46.908545+00:00","updated_at":"2026-05-18T00:24:46.908545+00:00"}