Existence of positive solutions for singular higher-order fractional differential equations  with infinite-points boundary conditions

LIMIN GUO; LISHAN LIU; YONGHONG WU

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Existence of positive solutions for singular higher-order fractional differential equations with infinite-points boundary conditions

LIMIN GUO 1, LISHAN LIU 2 *, YONGHONG WU 3

1. School of Mathematical Science, Qufu Normal University, Qufu 273165,

2. School of Mathematical Science, Qufu Normal University, Qufu 273165; Department of Mathematics and Statistics, Curtin University, Perth,

3. Department of Mathematics and Statistics, Curtin University, Perth,

*Correspondence author

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Funding: National Natural Science Foundation of China（No.11371221,11571296）

Opened online:17 May 2016

Accepted by: none

Citation: LIMIN GUO, LISHAN LIU, YONGHONG WU.Existence of positive solutions for singular higher-order fractional differential equations with infinite-points boundary conditions[OL]. [17 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4688813

In this paper, a class of singular fractional differential equations with infinite-points boundary conditions is considered. The fractional orders are involved in the nonlinearity of theboundary value problem and the nonlinearity is allowed to be singular with respect to not only the time variable but also the space variable. Firstly, we give Green's function and establish its properties. Then, we utilize the sequential technique and regularization to investigate the existence of positive solutions.

Keywords:Fractional differential equation; Singular problem; Infinite-points boundary conditions; Positive solution; Sequential techniques and regularization

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