{"paper":{"title":"Late-Time Fractional-Order Identification in Caputo Diffusion Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Niyaz Tokmagambetov","submitted_at":"2026-07-02T08:51:37Z","abstract_excerpt":"We study late-time identification of the Caputo order in a linear diffusion equation generated by a strictly positive self-adjoint operator with compact resolvent. For signed scalar observations \\(M_\\alpha(t)=\\sum_n a_nE_{\\alpha,1}(-\\lambda_nt^\\alpha)\\) satisfying \\(\\sum_n|a_n|/\\lambda_n<\\infty\\), we show that, after eigenspace grouping, every nontrivial observation has a finite first nonzero resolvent moment \\(S_m=\\sum_n a_n/\\lambda_n^m\\). A uniform differentiated large-argument expansion of the Mittag-Leffler factor yields eventual strict monotonicity of \\(\\alpha\\mapsto M_\\alpha(t)\\) on admi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01898","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/2607.01898/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"}