Local uniqueness of positive solutions for a coupled system of fractional differential equations with integral boundary conditions

• Published in: Advances in difference equations Vol. 2017; no. 1; pp. 1 - 12
• Main Authors: Yang, Chen, Zhai, Chengbo, Zhang, Lingling
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12.09.2017; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary conditions; Boundary value problems; coupled system of fractional boundary value problems; Difference and Functional Equations; Differential equations; Existence theorems; Fixed points (mathematics); Functional Analysis; integral boundary conditions; Integrals; local existence and uniqueness; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; positive solutions; Uniqueness; positive solutions; coupled system of fractional boundary value problems; local existence and uniqueness; 34B27; 26A33; integral boundary conditions; 34A08; 34B18
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-017-1343-7

In this paper, we study a coupled system of fractional boundary value problems subject to integral boundary conditions. By applying a recent fixed point theorem in ordered Banach spaces, we investigate the local existence and uniqueness of positive solutions for the coupled system. We show that the unique positive solution can be found in a product set, and that it can be approximated by constructing iterative sequences for any given initial point of the product set. As an application, an interesting example is presented to illustrate our main result.