{"paper":{"title":"A Kamenev-type oscillation result for a linear $(1+\\alpha)$--order fractional differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Donal O'Regan, Dumitru Baleanu, Octavian G. Mustafa","submitted_at":"2013-10-16T13:14:33Z","abstract_excerpt":"We investigate the eventual sign changing for the solutions of the linear equation $\\left(x^{(\\alpha)}\\right)^{\\prime}+q(t)x=0$, $t\\geq0$, when the functional coefficient $q$ satisfies the Kamenev-type restriction $\\limsup\\limits_{t\\rightarrow+\\infty}\\frac{1}{t^{\\varepsilon}}\\int_{t_0}^{t}(t-s)^{\\varepsilon}q(s)ds=+\\infty$ for some $\\varepsilon>2$, $t_{0}>0$. The operator $x^{(\\alpha)}$ is the Caputo differential operator and $\\alpha\\in(0,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4365","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"}