{"paper":{"title":"Stability by Lyapunov functions of Caputo fractional differential equations with non-instantaneous impulses","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. O'Regan, Ravi Agarwal, S. Hristova","submitted_at":"2015-12-17T20:52:42Z","abstract_excerpt":"The stability of the zero solution of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given noninstantaneous impulsive fractional differential equations. On one side this definition is a natural generalization of Caputo fractional Dini derivative of a function and on the other side it allows us the assumption for Lyapunov functions to be weakened to continuity. By appropriate examples it is shown the natura"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05772","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"}