{"paper":{"title":"On the local $M$-derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Capelas de Oliveira, J. Vanterler da C. Sousa","submitted_at":"2017-04-14T20:26:52Z","abstract_excerpt":"We introduce a new fractional derivative that generalizes the so-called alternative fractional derivative recently proposed by Katugampola. We denote this new differential operator by $\\mathscr{D}_{M}^{\\alpha,\\beta }$, where the parameter $\\alpha$, associated with the order, is such that $0<\\alpha<1$, $\\beta>0$ and $M$ is used to denote that the function to be derived involves a Mittag-Leffler function with one parameter. This new derivative satisfies some properties of integer-order calculus, e.g.\\ linearity, product rule, quotient rule, function composition and the chain rule. Besides as in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08186","kind":"arxiv","version":3},"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"}