{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T05:33:13Z","timestamp":1767677593946,"version":"3.48.0"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates a novel class of fractional Langevin equations, which introduces a time-varying p(t)-Laplacian operator and parameterized anti-periodic boundary conditions. This approach overcomes the limitations of traditional models characterized by constant diffusion exponents and fixed boundary locations. Under non-compactness conditions, the existence of solutions is established by applying Schaefer\u2019s fixed-point theorem, which significantly relaxes the conventional constraints on the nonlinear term. Moreover, by imposing a Lipschitz condition on the nonlinear term, a Ulam\u2013Hyers-type stability criterion for the coupled system is derived. This work not only extends the relevant stability theory but also provides a rigorous theoretical foundation for error control in practical applications. The effectiveness of the theoretical results is validated through numerical examples.<\/jats:p>","DOI":"10.3390\/axioms15010033","type":"journal-article","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T11:11:46Z","timestamp":1767352306000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations"],"prefix":"10.3390","volume":"15","author":[{"given":"Fangfang","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Yili Normal University, Yining 835000, China"},{"name":"Institute of Applied Mathematics, Yili Normal University, Yining 835000, China"}]},{"given":"Weimin","family":"Hu","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Yili Normal University, Yining 835000, China"}]},{"given":"Xiaoxiao","family":"Cui","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Yili Normal University, Yining 835000, China"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,1]]},"reference":[{"key":"ref_1","first-page":"530","article-title":"On the theory of Brownian motion","volume":"146","author":"Langevin","year":"1908","journal-title":"Comptes Rendus Acad. 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