Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions

Volume 10, Issue 1, pp 243--262 http://dx.doi.org/10.22436/jnsa.010.01.24

Publication Date: January 27, 2017 Submission Date: October 15, 2016

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Authors

Lishan Liu - School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China. - Department of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia. Hongdan Li - School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China. Chun Liu - School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China. Yonghong Wu - Department of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia.

Abstract

In this paper, we study the existence and uniqueness of positive solutions for a class of singular fractional differential systems with coupled integral boundary conditions. By using the properties of the Green function, the mixed monotone method and the fixed point theory in cones, we obtain the existence and uniqueness results for the problem. The results obtained herein generalize and improve some known results including singular and non-singular cases.

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Keywords

• Singular fractional differential equations
• Riemann-Stieltjes integral boundary value problem
• positive solution
• fixed point theorem in cone.

MSC

•  34B16
•  34B18
•  47H05

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