{"paper":{"title":"Existence and Uniqueness results for a class of Generalized Fractional Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Udita N. Katugampola","submitted_at":"2014-11-07T05:49:55Z","abstract_excerpt":"The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a new fractional derivative, \\[{}^\\rho \\mathcal{D}_a^\\alpha f (x) = \\frac{\\rho^{\\alpha-n+1}}{\\Gamma({n-\\alpha})} \\, \\bigg(x^{1-\\rho} \\,\\frac{d}{dx}\\bigg)^n \\int^x_a \\frac{\\tau^{\\rho-1} f(\\tau)}{(x^\\rho - \\tau^\\rho)^{\\alpha-n+1}}\\, d\\tau \\] which generalizes two familiar fractional derivatives, namely, the Riemann-Liouville and the Hadamard fractional derivatives to a single form. In this paper, we derive the existence and uniqueness results for a generalized fractional differential equation governed by the fractional derivative in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5229","kind":"arxiv","version":2},"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"}