Existence and uniqueness results for fractional Langevin equations on a star graph

Wei Zhang; Jifeng Zhang; Jinbo Ni; Wei Zhang; Jifeng Zhang; Jinbo Ni

doi:10.3934/mbe.2022448

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 9636-9657. doi: 10.3934/mbe.2022448

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Existence and uniqueness results for fractional Langevin equations on a star graph

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

Academic Editor: Feliz Manuel Barrão Minhós

Received: 06 May 2022 Revised: 23 June 2022 Accepted: 27 June 2022 Published: 04 July 2022

This paper discusses a class of fractional Langevin equations on a star graph with mixed boundary conditions. Using Schaefer's fixed point theorem and Banach contraction mapping principle, the existence and uniqueness of solutions are established. Finally, two examples are constructed to illustrate the application of the obtained results. This study provides new results that enrich the existing literature on the fractional boundary value problem for graphs.
- fractional Langevin equation,
- boundary value problem,
- star graph,
- fixed point theorem,
- existence and uniqueness
Citation: Wei Zhang, Jifeng Zhang, Jinbo Ni. Existence and uniqueness results for fractional Langevin equations on a star graph[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9636-9657. doi: 10.3934/mbe.2022448

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Abstract

This paper discusses a class of fractional Langevin equations on a star graph with mixed boundary conditions. Using Schaefer's fixed point theorem and Banach contraction mapping principle, the existence and uniqueness of solutions are established. Finally, two examples are constructed to illustrate the application of the obtained results. This study provides new results that enrich the existing literature on the fractional boundary value problem for graphs.

References

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