{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TAGLEXRUT7V5H352M6CUBUR2EI","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":"c2dd5d0f1aa97172fbe1d608a6f1c43f37f61b2a8fa06325eeaaeebd2d25f304","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-24T21:12:06Z","title_canon_sha256":"8ce3e4bee46b43ed258b75d3c96dd3af1ff461cac2a5aa7d23d325e59671301f"},"schema_version":"1.0","source":{"id":"1602.07713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07713","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07713v1","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07713","created_at":"2026-05-18T01:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"TAGLEXRUT7V5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TAGLEXRUT7V5H352","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TAGLEXRU","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:90aa4381797bdf2bf9db71e3199ab0c9e6d8e19b2bb8e5c577b7ab5f9b4e1a9e","target":"graph","created_at":"2026-05-18T01:04:28Z","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":"In this article we prove that if the $q-$fractional operator $(~_{q}\\nabla_{qa}^\\alpha y)(t)$ of order $0<\\alpha\\leq 1$ , $0<q<1$ and starting at some $qa \\in T_q=\\{q^k: k \\in \\mathbb{Z}\\}\\cup \\{0\\},~~a>0$ is positive such that $y(a) \\geq 0$, then $y(t)$ is $c_q(\\alpha)-$increasing, $c_q(\\alpha)=\\frac{1-q^\\alpha}{1-q}q^{1-\\alpha}$. Conversely, if y(t) is increasing and $y(a)\\geq 0$, then $(~_{q}\\nabla_{qa}^\\alpha y)(t)\\geq 0$. As an application, we proved a $q-$fractional version of the Mean-Value Theorem.","authors_text":"Bahaaeldin Abdalla, Juan J. Nieto, Thabet Abdeljawad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-24T21:12:06Z","title":"A monotonicity result for the $q-$fractional operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07713","kind":"arxiv","version":1},"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":"sha256:71c2f0949880008c2a3b33f71ae0fdf590f5190966158a665ee3d9ce8563efc9","target":"record","created_at":"2026-05-18T01:04:28Z","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":"c2dd5d0f1aa97172fbe1d608a6f1c43f37f61b2a8fa06325eeaaeebd2d25f304","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-24T21:12:06Z","title_canon_sha256":"8ce3e4bee46b43ed258b75d3c96dd3af1ff461cac2a5aa7d23d325e59671301f"},"schema_version":"1.0","source":{"id":"1602.07713","kind":"arxiv","version":1}},"canonical_sha256":"980cb25e349febd3efba678540d23a220790f9c8193dea83abec85c24c02219c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"980cb25e349febd3efba678540d23a220790f9c8193dea83abec85c24c02219c","first_computed_at":"2026-05-18T01:04:28.041626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:28.041626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NJ6iEGxGBFtXTZL8E5GwxKfbCUnQ6uqSRec+7JlNRgSol0lhkH8vEjRW/9/4RzEccpNHNnktXYvSA/VkxmQZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:28.042277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71c2f0949880008c2a3b33f71ae0fdf590f5190966158a665ee3d9ce8563efc9","sha256:90aa4381797bdf2bf9db71e3199ab0c9e6d8e19b2bb8e5c577b7ab5f9b4e1a9e"],"state_sha256":"2b6d964fa41bfdebe9a26fbb0d297c26800c88a7c1dea8b38799e81311a8b8b8"}