{"paper":{"title":"Fractional Calculus - A Commutative Method on Real Analytic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Matthew Parker","submitted_at":"2012-07-27T18:24:34Z","abstract_excerpt":"The traditional first approach to fractional calculus is via the Riemann-Liouville differintegral $_{a}D_{x}^{k}$. The intent of this paper will be to create a space $K$, pair of maps $g: C^{\\omega}(\\mathbb{R}) \\to K$ and $g': K \\to C^{\\omega}(\\mathbb{R}$), and operator $D^{k}: K \\to K$ such that the operator $D^{k}$ commutes with itself, the map $g$ embeds $C^{\\omega}(\\mathbb{R}$) isomorphically into $K$, and the following diagram commutes;\n  \\xymatrix{C^{\\omega}(\\mathbb{R}) \\ar[d]_{_{a}D_{x}^{k}} \\ar[r]^{g} & K \\ar[d]^{D^{k}}\n  C^{\\omega}(\\mathbb{R}) & K \\ar[l]^{g'}}\n  \\qquad This implies th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6610","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"}