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Math. 264 (2014) 65-70] is equivalent to classical differentiability. Precisely the fractional $\\alpha$-derivative of $f$ is the pointwise product $T_{\\alpha}f(x)=x^{1-\\alpha}f^{\\prime}(x)$, $x>0$. This simplifies the recent results concerning conformable fractional calculus."},"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":"1805.02309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-07T01:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"28751466c574e183900377515019465659bf9e62659e4cd006d8c758a5c0e6e8","abstract_canon_sha256":"cca335fcfdf3abcc5b3de82737ae1485994910edb0bb5235bf7347320b70e92d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:40.222155Z","signature_b64":"2iczwCZnglIObN39eluhbI2PSAvGaDDyL4g4nSk1z2zPqqdKjOXuJIPdoAQ1jgQYNGPJq7bNB+bSwJvZRDWwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf750bec21247eee1fb5ad26c13c267de7362c065c1ab47b41cf8bfce0c0a131","last_reissued_at":"2026-05-18T00:16:40.221580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:40.221580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Precise interpretation of the conformable fractional derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ahmed A. Abdelhakim","submitted_at":"2018-05-07T01:21:52Z","abstract_excerpt":"Let $\\alpha\\in\\,]0,1[$. We prove that the existence of the conformable fractional derivative $T_{\\alpha}f$ of a function $f:[0,\\infty[\\,\\longrightarrow \\mathbb{R}$ introduced by Khalil et al. in [R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65-70] is equivalent to classical differentiability. Precisely the fractional $\\alpha$-derivative of $f$ is the pointwise product $T_{\\alpha}f(x)=x^{1-\\alpha}f^{\\prime}(x)$, $x>0$. 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