{"paper":{"title":"Random-time processes governed by differential equations of fractional distributed order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Luisa Beghin","submitted_at":"2011-03-02T10:24:45Z","abstract_excerpt":"We analyze here different types of fractional differential equations, under the assumption that their fractional order $\\nu \\in (0,1] $ is random\\ with probability density $n(\\nu).$ We start by considering the fractional extension of the recursive equation governing the homogeneous Poisson process $N(t),t>0.$\\ We prove that, for a particular (discrete) choice of $n(\\nu)$, it leads to a process with random time, defined as $N(% \\widetilde{\\mathcal{T}}_{\\nu_{1,}\\nu_{2}}(t)),t>0.$ The distribution of the random time argument $\\widetilde{\\mathcal{T}}_{\\nu_{1,}\\nu_{2}}(t)$ can be expressed, for any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0386","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"}