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This model has been introduced by Laskin in quantum physics \\cite{laskin}. We establish local well-posedness and ill-posedness in Sobolev spaces for power-type nonlinearities."},"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":"1501.01414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T09:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"6f6149aba294f220e289381a4b7352294159a1337913199baab8fa92e3b8900f","abstract_canon_sha256":"4853db1decde8786c4e33bb9d84395d87953cce28f1a533f9ab6f7892c8f4df7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:54.299031Z","signature_b64":"sCriiwUDAri8Z2+X7IpFvpZMFghAQvrdWqqnH36LRGOGmxNRg7n05drvqKx3IkL+vI+rggWFhMrAgGQTPOgdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24cdddbec4783ff1c325b024746ce57ae92660ff2f80f90927fd05099a88b667","last_reissued_at":"2026-05-18T02:29:54.298616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:54.298616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Fractional Schrodinger Equations in sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yannick Sire, Younghun Hong","submitted_at":"2015-01-07T09:39:06Z","abstract_excerpt":"Let $\\sigma\\in(0,1)$ with $\\sigma\\neq\\frac{1}{2}$. 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