Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions

Boundary value problems

Yonghong Wu²  Limin Guo²  Lishan Liu³ 

[1] Department of Mathematics and Statistics, Curtin University, Perth, Australia;School of Mathematical Sciences, Qufu Normal University, Qufu, People’s Republic of China

关键词: fractional differential system;    integral boundary conditions;    singular problem;    iterative positive solution;    mixed monotone operator;    26A33;    34A08;    34B15;    34B16;    34B18;   

DOI  :  10.1186/s13661-016-0652-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The uniqueness of positive solution for a class of singular fractional differential system with integral boundary conditions is considered in this paper and many types of equation system are contained in this equation system because there are many parameters which can be changeable in this equation system. The fractional orders are involved in the nonlinearity of the boundary value problem and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable. The existence of uniqueness of positive solution is mainly obtained by fixed point theorem of mixed monotone operator and the positive solution of equation system is dependent on λ. An iterative sequence and convergence rate are given which are important for practical application and an example is given to demonstrate the validity of our main results.

【 授权许可】

CC BY