【摘要】 研究了一类分数阶q-差分方程多点边值问题,其中控制函数含有分数阶导数.首先通过变换将该问题转化为带有分数阶积分控制的边值问题,并分析了格林函数的一些性质;其次利用Arzela-Ascoli不动点定理及上下解方法,证明了该方程正解的存在性;最后通过实例验证了本文所得结论的正确性.更多还原

【Abstract】 We study a class of the boundary value problems of fractional q-difference equations.Here,the fractional derivative is contained in control function.Firstly,we transform the problem into a boundary value problem with fractional integrals control and analyze some properties of the Green function.Secondly,the existence of the solutions of the equation are proved by using the Arzela-Ascoli fixed point theorem in Banach space and upper and lower solution method.Finally,we give a example to illustrate our results.更多还原