{"paper":{"title":"On the $\\mathbf{\\rm\\Psi}-$fractional integral and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa","submitted_at":"2017-10-10T16:36:09Z","abstract_excerpt":"Motivated by the ${\\rm \\Psi}$-Riemann-Liouville $({\\rm \\Psi-RL})$ fractional derivative and by the ${\\rm \\Psi}$-Hilfer $({\\rm \\Psi-H})$ fractional derivative, we introduced a new fractional operator the so-called $\\rm\\Psi-$fractional integral. We present some important results by means of theorems and in particular, that the $\\rm\\Psi-$fractional integration operator is limited. In this sense, we discuss some examples, in particular, involving the Mittag-Leffler $({\\rm M-L})$ function, of paramount importance in the solution of population growth problem, as approached. On the other hand, we rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03712","kind":"arxiv","version":3},"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"}