THE EXISTENCE OF NONTRIVIAL SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Yan Bai; Weihua Jiang; Yanping Guo; Yunhong Li; Yujing Liu

doi:10.11948/20200202

2021 Volume 11 Issue 2

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Yan Bai, Weihua Jiang, Yanping Guo, Yunhong Li, Yujing Liu. THE EXISTENCE OF NONTRIVIAL SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 1017-1028. doi: 10.11948/20200202

Citation:

Yan Bai, Weihua Jiang, Yanping Guo, Yunhong Li, Yujing Liu. THE EXISTENCE OF NONTRIVIAL SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 1017-1028. doi: 10.11948/20200202

THE EXISTENCE OF NONTRIVIAL SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

1.
College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, China

Corresponding author: Email address: jianghua64@163.com(W. Jiang)
Fund Project: The authors were supported by National Natural Science Foundation of China (11775169) and National Science Foundation of Hebei Province (A2018208171)

Abstract

Abstract

By using the theory of degree, the existence of nontrivial solution for boundary value problem of nonlinear fractional differential equation is investigated. In order to get this conclusion, we make use of Laplace transform to obtain the conditions that the eigenvalues satisfy. Then, for three different specific problems, we use Matlab software to calculate the eigenvalues. This is the fundamental skill that Leray-Schauder degree theorem can be used.
- Fractional differential equation /
- eigenvalue /
- Green's function /
- Leray-Schauder degree
MSC: 26A33, 34A08, 34B15

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References

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