{"paper":{"title":"Asymptotic integration of $(1+\\alpha)$-order fractional differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dumitru Baleanu, Octavian G. Mustafa, Ravi P. Agarwal","submitted_at":"2010-10-22T11:28:52Z","abstract_excerpt":"\\noindent{\\bf Abstract} We establish the long-time asymptotic formula of solutions to the $(1+\\alpha)$--order fractional differential equation ${}_{0}^{\\>i}{\\cal O}_{t}^{1+\\alpha}x+a(t)x=0$, $t>0$, under some simple restrictions on the functional coefficient $a(t)$, where ${}_{0}^{\\>i}{\\cal O}_{t}^{1+\\alpha}$ is one of the fractional differential operators ${}_{0}D_{t}^{\\alpha}(x^{\\prime})$, $({}_{0}D_{t}^{\\alpha}x)^{\\prime}={}_{0}D_{t}^{1+\\alpha}x$ and ${}_{0}D_{t}^{\\alpha}(tx^{\\prime}-x)$. Here, ${}_{0}D_{t}^{\\alpha}$ designates the Riemann-Liouville derivative of order $\\alpha\\in(0,1)$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4675","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"}