{"paper":{"title":"A New Approach to Generalized Fractional Derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Udita N. Katugampola","submitted_at":"2011-06-06T06:21:57Z","abstract_excerpt":"The author \\mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \\[ \\big({}^\\rho \\mathcal{I}^\\alpha_{a+}f\\big)(x) = \\frac{\\rho^{1- \\alpha }}{\\Gamma({\\alpha})} \\int^x_a \\frac{\\tau^{\\rho-1} f(\\tau) }{(x^\\rho - \\tau^\\rho)^{1-\\alpha}}\\, d\\tau, \\] which generalizes the well-known Riemann-Liouville and the Hadamard fractional integrals. In this paper we present a new fractional derivative which generalizes the familiar Riemann-Liouville and the Hadamard fractional derivatives to a single form. We also obtain two representations of the generalized d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0965","kind":"arxiv","version":5},"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"}