{"paper":{"title":"About the existence of solutions for a hybrid nonlinear generalized fractional pantograph equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B.Lopez, E.T.Karimov, K.Sadarangani","submitted_at":"2016-05-29T06:57:58Z","abstract_excerpt":"The main purpose of this paper is to study the existence of solutions for the following hybrid nonlinear fractional pantograph equation $$ \\left\\{\\begin{aligned} &D_{0+}^\\alpha \\left[\\frac{x(t)}{f(t,x(t),x(\\varphi(t)))}\\right]=g(t,x(t),x(\\rho(t))),\\,\\,0<t<1\\\\ &x(0)=0, \\end{aligned} \\right. $$ where $\\alpha\\in (0,1)$, $\\varphi$ and $\\rho$ are functions from $[0,1]$ into itself and $D_{0+}^\\alpha$ denotes the Riemann-Liouville fractional derivative. The main tool of our study is a generalization of Darbo's fixed point theorem associated to measures of non-compactness. Also, we present an example"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08972","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"}