FRACTIONAL DISSIPATIVE STURM-LIOUVILLE PROBLEMS WITH DISCONTINUITY AND EIGEN-DEPENDENT BOUNDARY CONDITIONS

Qiyuan Meng; Xiaoling Hao; Kun Li

doi:10.11948/20220248

2023 Volume 13 Issue 1

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Qiyuan Meng, Xiaoling Hao, Kun Li. FRACTIONAL DISSIPATIVE STURM-LIOUVILLE PROBLEMS WITH DISCONTINUITY AND EIGEN-DEPENDENT BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 445-457. doi: 10.11948/20220248

Citation:

Qiyuan Meng, Xiaoling Hao, Kun Li. FRACTIONAL DISSIPATIVE STURM-LIOUVILLE PROBLEMS WITH DISCONTINUITY AND EIGEN-DEPENDENT BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 445-457. doi: 10.11948/20220248

FRACTIONAL DISSIPATIVE STURM-LIOUVILLE PROBLEMS WITH DISCONTINUITY AND EIGEN-DEPENDENT BOUNDARY CONDITIONS

1.
Math., Dept., Inner Mongolia University, Hohhot, 010021, China
2.
Math., Dept., Qufu Normal University, Qufu, 276826, China

Corresponding author: Email: xlhao1883@163.com.(X. Hao)

Abstract

Abstract

This paper studies two main fractional discontinuous dissipative Sturm-Liouville type boundary-value problems with boundary conditions and transmission conditions. In both types of research, with the aid of the operator theory, we define different classes of new inner products by combining the parameters in the boundary and transmission conditions, then the boundary value problems are transferred to operators in the Hilbert spaces such that the eigenvalues and eigenfunctions of the main problem coincide with those of operators. And we prove those of operators are dissipative. Moreover, the fundamental solutions are constructed and the uniqueness of the solutions of the problem is also given.
- Fractional Sturm-Liouville problem /
- dissipative operator /
- eigenparameter dependent boundary conditions /
- transmission conditions
MSC: 34B24, 34L20, 34L05

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References

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