一类分数阶q-差分系统边值问题解的存在性

Existence of solutions for boundary value problems with a coupled system of fractional q- differences

研究了一类带有分数阶边值条件的分数阶q-差分系统正解的存在性.首先,给出了该问题解的表达式,并分析了格林函数的性质,然后运用基本的不动点定理证明了该问题正解的存在性和唯一性.最后,用具体例子验证了文中主要结论的正确性.

We study the existence of positive solutions for a fractional q-difference system with a fractional boundary condition.Firstly,expressions of the solutions are presented,and properties of the Green function are analyzed.Secondly,the existence and uniqueness of the positive solutions of the problem are proved by basic fixed point theorem.Finally,the main conclusions are verified by some specific examples.