Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations

Hu, Fangfang; Hu, Weimin; Cui, Xiaoxiao

doi:10.3390/axioms15010033

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Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations

by

Fangfang Hu

^1,2,

Weimin Hu

^2,* and

Xiaoxiao Cui

^2,*

¹

School of Mathematics and Statistics, Yili Normal University, Yining 835000, China

²

Institute of Applied Mathematics, Yili Normal University, Yining 835000, China

^*

Authors to whom correspondence should be addressed.

Axioms 2026, 15(1), 33; https://doi.org/10.3390/axioms15010033 (registering DOI)

Submission received: 2 December 2025 / Revised: 28 December 2025 / Accepted: 29 December 2025 / Published: 1 January 2026

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Abstract

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’s 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–Hyers-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.

Keywords: fractional Langevin equation; p(t)-Laplacian operator; parameterized anti-periodic boundary value problems; Ulam–Hyers stability; Schaefer fixed point theorem; existence of solutions

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MDPI and ACS Style

Hu, F.; Hu, W.; Cui, X. Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations. Axioms 2026, 15, 33. https://doi.org/10.3390/axioms15010033

AMA Style

Hu F, Hu W, Cui X. Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations. Axioms. 2026; 15(1):33. https://doi.org/10.3390/axioms15010033

Chicago/Turabian Style

Hu, Fangfang, Weimin Hu, and Xiaoxiao Cui. 2026. "Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations" Axioms 15, no. 1: 33. https://doi.org/10.3390/axioms15010033

APA Style

Hu, F., Hu, W., & Cui, X. (2026). Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations. Axioms, 15(1), 33. https://doi.org/10.3390/axioms15010033

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Parameterized Anti-Periodic Problems: Existence and Ulam-Hyers Stability for Fractional p(t)-Laplacian Langevin Equations

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