Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

• Published in: Boundary value problems Vol. 2018; no. 1; pp. 1 - 17
• Main Authors: He, Jianxin, Zhang, Xinguang, Liu, Lishan, Wu, Yonghong, Cui, Yujun
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12.12.2018; Hindawi Limited; SpringerOpen
• Subjects: Analysis; Approximations and Expansions; Asymptotic analysis; Asymptotic properties; Boundary conditions; Difference and Functional Equations; Differential equations; Existence theorems; Fixed points (mathematics); Fractional differential equation; Mathematics; Mathematics and Statistics; Nonlocal boundary conditions; Ordinary Differential Equations; Partial Differential Equations; Upper and lower solutions method; Fractional differential equation; Upper and lower solutions method; Nonlocal boundary conditions; Asymptotic analysis
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-018-1109-5

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.