New unique existence criteria for higher-order nonlinear singular fractional differential equations
Articles
Hui Wang
Taiyuan University of Technology
Lingling Zhang
Taiyuan University of Technology
Xiaoqiang Wang
Florida State University
Published 2018-12-14
https://doi.org/10.15388/NA.2019.1.6
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Keywords

singular fractional differential equations
three-point boundary value problem
existence and uniqueness
fixed point theorem
sum-type operator

How to Cite

Wang, H., Zhang, L. and Wang, X. (2018) “New unique existence criteria for higher-order nonlinear singular fractional differential equations”, Nonlinear Analysis: Modelling and Control, 24(1), pp. 95–120. doi:10.15388/NA.2019.1.6.

Abstract

In this paper, a nonlinear three-point boundary value problem of higher-order singular fractional differential equations is discussed. By applying the properties of Green function and some fixed point theorems for sum-type operator on cone, some new criteria on the existence and uniqueness of solutions are obtained. Moreover, two iterative sequences are given for uniformly approximating the positive solution, which are important for practical application. At last, we give two examples to illustrate the main results.

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