一类带积分边值条件的高阶时滞分数阶微分方程解的存在性

Existence of the solutions for integral boundary value problems to a class of higher order fractional differential equations with delay

研究了一类带有积分边界条件的高阶分数阶时滞微分方程解的存在性和存在唯一性问题.首先建立了这类边值问题的格林函数,进而将该问题转化为相应积分算子的不动点问题,利用Leray-Schauder二择一定理得到了该边值问题解存在的充分条件,其次给出了问题解存在唯一性的充分条件,最后通过一个具体的例子对结果进行了说明,补充和完善了已有的研究结果.

The integral boundary value problem to a class of higher order fractional differential equation with delay is studied.Firstly,the green function of this kind boundary value problem is established,and then the problem is changed into an integral operator’s fixed point.By using Leray-Schauder nonlinear alternative theorem,some sufficient conditions on the existence of solutions for this boundary value problem are obtained.Secondly,some sufficient conditions on the existence and uniqueness about solutions are also established.Finally,one specific example is given to illustrate the results.Some known research results are extended and improved.