An upper-lower solution method for the eigenvalue problem of Hadamard-type singular fractional differential equation
Articles
Xinguang Zhang
Yantai University
https://orcid.org/0000-0001-9250-6823
Dezhou Kong
Shandong Agricultural University
Hui Tian
Yantai University
https://orcid.org/0000-0001-7904-6738
Yonghong Wu
Curtin University of Technology
https://orcid.org/0000-0003-1028-1785
Benchawan Wiwatanapataphee
Curtin University of Technology
https://orcid.org/0000-0003-1875-6984
Published 2022-05-10
https://doi.org/10.15388/namc.2022.27.27491
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Keywords

Hadamard-type fractional differential equation
upper-lower solution method, eigenvalue problem
singularity

How to Cite

Zhang X., Kong D., Tian H., Wu Y. and Wiwatanapataphee B. (2022) “An upper-lower solution method for the eigenvalue problem of Hadamard-type singular fractional differential equation”, Nonlinear Analysis: Modelling and Control, 27(4), pp. 789-802. doi: 10.15388/namc.2022.27.27491.

Abstract

In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fixed point theorem. The main contribution of this work is on tackling the nonlinearity which possesses singularity on some space variables.

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