带有分数阶边值条件的分数阶差分方程的正解

Existence of positive solution for a fractional difference equations with fractional boundary value condition

研究了一类带有分数阶边值条件的分数阶差分方程正解的存在性问题.首先利用分数阶差分方程理论和边值条件给出了解的结构,其次分析了Green函数的一些性质,最后利用锥上的不动点定理证明了该问题正解的存在性.

We study the existence of positive solutions of the boundary value problem for a fractional difference equation with fractional boundary value condition.Firstly,according to the theory of fractional difference equation and its boundary conditions,we got the structure of solutions,then analyze some properties of the Green’s function,at last,the existence of the positive solutions of the problem is proved by using the fixed point theorem in cones.