{"paper":{"title":"On well-posedness of vector-valued fractional differential-difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Lizama, Luciano Abadias, M. Pilar Velasco, Pedro J. Miana","submitted_at":"2016-06-16T15:57:28Z","abstract_excerpt":"We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \\begin{equation*} \\left\\{ \\begin{array}{rll} \\Delta^{\\alpha} u(n) &= Au(n+2) + f(n,u(n)), \\quad n \\in \\mathbb{N}_0, \\,\\, 1< \\alpha \\leq 2; u(0) &= u_0; u(1) &= u_1, \\end{array} \\right. \\end{equation*} where $A$ is an closed linear operator defined on a Banach space $X$. Our ideas are inspired on the Poisson distribution as a tool to sampling fractional differential operators into fractional differences. Using our abstract approach, we are able to show e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05237","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"}