{"paper":{"title":"Two families of novel second-order fractional numerical formulas and their applications to fractional differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Baoli Yin, Hong Li, Yang Liu, Zhimin Zhang","submitted_at":"2019-06-04T07:23:26Z","abstract_excerpt":"In this article, we introduce two families of novel fractional $\\theta$-methods by constructing some new generating functions to discretize the Riemann-Liouville fractional calculus operator $\\mathit{I}^{\\alpha}$ with a second order convergence rate. A new fractional BT-$\\theta$ method connects the fractional BDF2 (when $\\theta=0$) with fractional trapezoidal rule (when $\\theta=1/2$), and another novel fractional BN-$\\theta$ method joins the fractional BDF2 (when $\\theta=0$) with the second order fractional Newton-Gregory formula (when $\\theta=1/2$). To deal with the initial singularity, corre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01242","kind":"arxiv","version":2},"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/1906.01242/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"}