{"paper":{"title":"Fractional calculus of variations for a combined Caputo derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres","submitted_at":"2011-09-21T22:15:28Z","abstract_excerpt":"We generalize the fractional Caputo derivative to the fractional derivative ${{^CD}^{\\alpha,\\beta}_{\\gamma}}$, which is a convex combination of the left Caputo fractional derivative of order $\\alpha$ and the right Caputo fractional derivative of order $\\beta$. The fractional variational problems under our consideration are formulated in terms of ${{^CD}^{\\alpha,\\beta}_{\\gamma}}$. The Euler-Lagrange equations for the basic and isoperimetric problems, as well as transversality conditions, are proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4664","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"}