{"paper":{"title":"Growth Equation of the General Fractional Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Anatoly N. Kochubei, Yuri Kondratiev","submitted_at":"2019-07-11T14:59:31Z","abstract_excerpt":"We consider the Cauchy problem $(\\mathbb D_{(k)} u)(t)=\\lambda u(t)$, $u(0)=1$, where $\\mathbb D_{(k)}$ is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory {\\bf 71} (2011), 583--600), $\\lambda >0$. The solution is a generalization of the function $t\\mapsto E_\\alpha (\\lambda t^\\alpha)$ where $0<\\alpha <1$, $E_\\alpha$ is the Mittag-Leffler function. The asymptotics of this solution, as $t\\to \\infty$, is studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05290","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"}