{"paper":{"title":"The Dissipative Effect of Caputo--Time-Fractional Derivatives and its Implications for the Solutions of Nonlinear Wave Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.PS","authors_text":"J. E. Mac\\'ias-D\\'iaz, Jes\\'us Cuevas-Maraver, Julia Cantis\\'an, Panayotis G. Kevrekidis, Tassos Bountis","submitted_at":"2024-06-13T08:17:30Z","abstract_excerpt":"In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional differential equations describing physical systems, whose time evolution for integer derivatives has a time-honored conservative form. This observation, although known to the general mathematical community, has not, in our view, been satisfactorily addressed. More specifically, we follow the recent exploration of Caputo-Riesz time-space-fractional nonlinear wave equation, in which two of the present authors introduced an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.08912","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/2406.08912/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"}