DISCONTINUOUS FRACTIONAL BOUNDARY VALUE PROBLEMS WITH ORDER $ \alpha\in (1,2) $

Jinwen Wu; Xiaoling Hao; Kun Li

doi:10.11948/20240478

2025 Volume 15 Issue 5

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Jinwen Wu, Xiaoling Hao, Kun Li. DISCONTINUOUS FRACTIONAL BOUNDARY VALUE PROBLEMS WITH ORDER $ \alpha\in (1,2) $[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2866-2883. doi: 10.11948/20240478

Citation:

Jinwen Wu, Xiaoling Hao, Kun Li. DISCONTINUOUS FRACTIONAL BOUNDARY VALUE PROBLEMS WITH ORDER $ \alpha\in (1,2) $[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2866-2883. doi: 10.11948/20240478

DISCONTINUOUS FRACTIONAL BOUNDARY VALUE PROBLEMS WITH ORDER $ \alpha\in (1,2) $

1.
Department of Mathematics, Inner Mongolia University, Hohhot 010021, China
2.
Department of Mathematics, Qufu Normal University, Qufu 276826, China

Author Bio: Email: 32236074@mail.imu.edu.cn(J. Wu); Email: qslikun@qfnu.edu.cn(K. Li)
Corresponding author: Xiaoling Hao, xlhao1883@163.com(X. Hao)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12361027, 12401160) and the Natural Science Foundation of Shandong Province (No. ZR2024MA020)

Abstract

Abstract

This paper focuses on investigating the discontinuous fractional Sturm-Liouville problem equipped with a transmission condition of order $ \alpha \in(1,2) $. Through rigorous analysis, it is demonstrated that the eigenvalues and their corresponding eigenfunctions of this problem coincide with those of the constructed operator in Hilbert space. Furthermore, a necessary and sufficient condition for the existence of eigenvalues is established, providing a theoretical foundation for the spectral characterization of such fractional boundary value problems.
- Sturm-Liouville problem /
- eigenvalues /
- fractional boundary conditions /
- fractional transmission conditions
MSC: 34B24, 34L20, 34L05

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References

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