SMALLEST EIGENVALUES AND THE EXISTENCE RESULT FOR THE BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS

Caixia Guo; Jianmin Guo; Shugui Kang; Huapeng Li

doi:10.11948/20220365

2023 Volume 13 Issue 4

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Caixia Guo, Jianmin Guo, Shugui Kang, Huapeng Li. SMALLEST EIGENVALUES AND THE EXISTENCE RESULT FOR THE BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2074-2088. doi: 10.11948/20220365

Citation:

Caixia Guo, Jianmin Guo, Shugui Kang, Huapeng Li. SMALLEST EIGENVALUES AND THE EXISTENCE RESULT FOR THE BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2074-2088. doi: 10.11948/20220365

SMALLEST EIGENVALUES AND THE EXISTENCE RESULT FOR THE BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS

1.
School of Mathematics and Statistics, Shanxi Datong University, Datong, 037009, China

Author Bio: Email: iris-gcx@163.com(C. Guo); Email: dtdxguojianmin@163.com(J. Guo); Email: dtkangshugui@126.com(S. Kang)
Corresponding author: Email: lihuaa1_0@163.com(H. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (11871314), Science and Technology Innovation Project of Colleges and Universities in Shanxi Province (2020L0475), Applied Foundational Research Project of the Datong Pingcheng District Science and Technology Bureau (201906, 202106) and Doctoral Foundation Project of Shanxi Datong University (2018-B-25)

Abstract

Abstract

In this paper, we first discuss the existence of smallest eigenvalues of fractional boundary value problems. Then we consider the existence of at least one positive solution for a class of nonlinear boundary value problem of fractional differential system. Compared with the existing methods, our analysis relies on the fixed point index theorem in a Cartesian product of two cones. We further construct two special operators to compute straightforwardly the fixed point index in a suitable cone. Finally, we present an illustrative example to support our main result.
- Fractional differential system /
- eigenvalues /
- Green's function /
- positive solution /
- fixed point index.
MSC: 34A08, 34K30

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