On the existence, uniqueness, and Ulam-Hyers stability of fractional Langevin equations with multi-point closed boundary conditions

Wei Zhang; Jianing Xu; Jinbo Ni; Wei Zhang; Jianing Xu; Jinbo Ni

doi:10.3934/nhm.2026079

Networks and Heterogeneous Media

2026, Volume 21, Issue 6: 2084-2107. doi: 10.3934/nhm.2026079

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Research article

On the existence, uniqueness, and Ulam-Hyers stability of fractional Langevin equations with multi-point closed boundary conditions

School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China

Received: 17 April 2026 Revised: 06 October 2026 Accepted: 13 October 2026 Published: 21 October 2026

This paper investigates the existence and uniqueness of mild solutions for a class of fractional Langevin equations subject to multi-point closed boundary conditions. By applying Krasnosel'skii fixed point theorem and the Banach contraction mapping principle, we establish sufficient conditions which ensure existence and uniqueness. Furthermore, we analyze the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the solutions within this framework. Illustrative examples are provided to demonstrate the applicability of the main results and to verify the stated hypotheses.
- fractional Langevin equation,
- multi-point closed boundary conditions,
- fixed point theorem,
- existence and uniqueness,
- Ulam-type stability
Citation: Wei Zhang, Jianing Xu, Jinbo Ni. On the existence, uniqueness, and Ulam-Hyers stability of fractional Langevin equations with multi-point closed boundary conditions[J]. Networks and Heterogeneous Media, 2026, 21(6): 2084-2107. doi: 10.3934/nhm.2026079

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Abstract

This paper investigates the existence and uniqueness of mild solutions for a class of fractional Langevin equations subject to multi-point closed boundary conditions. By applying Krasnosel'skii fixed point theorem and the Banach contraction mapping principle, we establish sufficient conditions which ensure existence and uniqueness. Furthermore, we analyze the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the solutions within this framework. Illustrative examples are provided to demonstrate the applicability of the main results and to verify the stated hypotheses.

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