The Green’s function of a class of two-term fractional differential equation boundary value problem and its applications

Advances in Difference Equations

article

Wang, Yongqing¹ 

[1] School of Mathematical Sciences, Qufu Normal University

关键词: Two-term fractional differential equation;    Boundary value problems;    Green’s function;    Positive solution;    Singularity;   

DOI  :  10.1186/s13662-020-02549-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we consider a Riemann–Liouville type two-term fractional differential equation boundary value problem. Some positive properties of the Green’s function are deduced by using techniques of analysis. As application, we obtain the existence and multiplicity of positive solutions for a fractional boundary value problem under conditions that the nonlinearity $f(t,x)$ may change sign and may be singular at $t = 0,1$ and $x=0$, and we also obtain the uniqueness results of positive solution for a singular problem by means of the monotone iterative technique.

【 授权许可】

CC BY