{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DYFFNB3OTM6PLWYPRBPKXS2N5E","short_pith_number":"pith:DYFFNB3O","schema_version":"1.0","canonical_sha256":"1e0a56876e9b3cf5db0f885eabcb4de927f3b262a0c46074a43ee8791aac9ee1","source":{"kind":"arxiv","id":"1502.06014","version":1},"attestation_state":"computed","paper":{"title":"Conformable Fractional Semigroups of Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.FA","authors_text":"Mohammed AL Horani, Roshdi Khalil, Thabet Abdeljawad","submitted_at":"2014-11-21T11:55:01Z","abstract_excerpt":"Let $X$ be a Banach space, and $T:[0,\\infty)\\rightarrow {\\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\\{T(t)\\}_{t\\ge 0}\\subseteq {% \\mathcal{L}}(X,X)$ is called a one-parameter semigroup if $T(s+t)=T(s)T(t),$ and $T(0)=I,$ the identity operator on $X.$ The infinitesimal generator of the semigroup is the derivative of the semigroup at $t=0.$ The object of this paper is to introduce a (conformable) fractional semigroup of operators whose generator will be the fractional derivative of the semigroup at $t=0.$ The basic properties of such semigroups will be studied."},"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":"1502.06014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-21T11:55:01Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"b596bc5e967e69a74bcd61cd668476a9b5b9b0075dc5961c29d4c478292a90cf","abstract_canon_sha256":"944da3b3e4279157809434abced47c105c4f9ad871165f4a7cb0d4e07b5bda72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.332210Z","signature_b64":"txAwAMxvulZr53XGj4YoVzj4+cO0Pmc2vSF1WHXEjXL43S0r9LA9rz04ljdxrTVB1iwVxnAW6uO9DB10e0VuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e0a56876e9b3cf5db0f885eabcb4de927f3b262a0c46074a43ee8791aac9ee1","last_reissued_at":"2026-05-18T01:04:30.331646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.331646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformable Fractional Semigroups of Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.FA","authors_text":"Mohammed AL Horani, Roshdi Khalil, Thabet Abdeljawad","submitted_at":"2014-11-21T11:55:01Z","abstract_excerpt":"Let $X$ be a Banach space, and $T:[0,\\infty)\\rightarrow {\\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\\{T(t)\\}_{t\\ge 0}\\subseteq {% \\mathcal{L}}(X,X)$ is called a one-parameter semigroup if $T(s+t)=T(s)T(t),$ and $T(0)=I,$ the identity operator on $X.$ The infinitesimal generator of the semigroup is the derivative of the semigroup at $t=0.$ The object of this paper is to introduce a (conformable) fractional semigroup of operators whose generator will be the fractional derivative of the semigroup at $t=0.$ The basic properties of such semigroups will be studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06014","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":"1502.06014","created_at":"2026-05-18T01:04:30.331721+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06014v1","created_at":"2026-05-18T01:04:30.331721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06014","created_at":"2026-05-18T01:04:30.331721+00:00"},{"alias_kind":"pith_short_12","alias_value":"DYFFNB3OTM6P","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DYFFNB3OTM6PLWYP","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DYFFNB3O","created_at":"2026-05-18T12:28:25.294606+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/DYFFNB3OTM6PLWYPRBPKXS2N5E","json":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E.json","graph_json":"https://pith.science/api/pith-number/DYFFNB3OTM6PLWYPRBPKXS2N5E/graph.json","events_json":"https://pith.science/api/pith-number/DYFFNB3OTM6PLWYPRBPKXS2N5E/events.json","paper":"https://pith.science/paper/DYFFNB3O"},"agent_actions":{"view_html":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E","download_json":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E.json","view_paper":"https://pith.science/paper/DYFFNB3O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06014&json=true","fetch_graph":"https://pith.science/api/pith-number/DYFFNB3OTM6PLWYPRBPKXS2N5E/graph.json","fetch_events":"https://pith.science/api/pith-number/DYFFNB3OTM6PLWYPRBPKXS2N5E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E/action/storage_attestation","attest_author":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E/action/author_attestation","sign_citation":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E/action/citation_signature","submit_replication":"https://pith.science/pith/DYFFNB3OTM6PLWYPRBPKXS2N5E/action/replication_record"}},"created_at":"2026-05-18T01:04:30.331721+00:00","updated_at":"2026-05-18T01:04:30.331721+00:00"}