{"paper":{"title":"On new types of fractional operators and applications","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bessem Samet, Mohamed Jleli","submitted_at":"2018-02-22T06:59:56Z","abstract_excerpt":"We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\\int_x^\\infty \\frac{e^{-t}}{t}\\,dt,\\quad x>0, $$ and the other is defined via the special function $$ \\mathcal{S}(x)=e^{-x} \\int_0^\\infty \\frac{x^{s-1}}{\\Gamma(s)}\\,ds,\\quad x>0. $$ We establish different properties of these operators, and we study the relationship between the fractional integrals of first kind and the fractional integrals of second kind. Next, we introduce a new concept of fractional derivative of order $\\alpha>0$, which is defined via the fractional int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03520","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"}