{"paper":{"title":"Dynamic-memory fractional calculus via generator-based memory construction: operational theory, semigroup structure, and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jehad Alzabut","submitted_at":"2026-05-25T21:02:59Z","abstract_excerpt":"Most generalized fractional operators rely on prescribed memory kernels, restricting hereditary behavior to predefined forms and limiting flexibility in modeling diverse memory effects. Motivated by these limitations, this paper develops a generator-based framework for fractional calculus in which memory laws are systematically generated through a dynamic memory generator in the Laplace domain. The resulting construction produces dynamic-memory kernels via inverse Laplace transforms, leading to generalized dynamic-memory fractional integrals together with Riemann--Liouville and Caputo dynamic-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26326","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/2605.26326/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"}