{"paper":{"title":"Beta-weighted non-local differential operators and related stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. Vaz, L. Beghin, N. Leonenko, T. Simon","submitted_at":"2026-06-02T13:47:30Z","abstract_excerpt":"In this work we introduce a class of non-local differential operators defined through a beta-weighted averaging of the ordinary derivative. We investigate their analytical properties and establish connections with the Caputo and Erd\\'elyi-Kober operators. Differential equations involving the beta-weighted derivative are studied by Mellin transform methods, leading to solutions represented in terms of Barnes G-functions and a new class of G-hypergeometric functions. We also analyze asymptotic properties, Laplace transforms, and the second-order equation involving the sequential beta-weighted de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03661","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03661/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}