{"paper":{"title":"New fractional integral unifying six existing fractional integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Udita N. Katugampola","submitted_at":"2016-12-22T16:48:32Z","abstract_excerpt":"In this paper we introduce a new fractional integral that generalizes six existing fractional integrals, namely, Riemann-Liouville, Hadamard, Erd\\'elyi-Kober, Katugampola, Weyl and Liouville fractional integrals in to one form. Such a generalization takes the form \\[\n  \\left({}^{\\rho}\\mathcal{I}^{\\alpha, \\beta}_{a+;\\eta, \\kappa}f\\right)(x)=\\frac{\\rho^{1-\\beta}x^{\\kappa}}{\\Gamma(\\alpha)}\\int_a^x \\frac{\\tau^{\\rho \\eta +\\rho-1}}{(x^\\rho-\\tau^\\rho)^{1-\\alpha}}f(\\tau)\\text{d}\\tau, \\quad 0\\leq a < x < b \\leq \\infty. \\] A similar generalization is not possible with the Erd\\'elyi-Kober operator though"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08596","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"}