分数阶微分方程多点边值问题正解的存在唯一性

摘要

To study the exisence and uniqueness of stutions for the fractional differential equation boundary value problem. The existence and uniqueness of positive solutions for a class of multi-point fractional differential equation boundary value problem were obtained by means of fixed point theorem of a sum operator and the properties of Green function. An iterative scheme to approximate the solution was constructed and an estimation of the positive solution were also established. An application was given as an example.%为了研究分数阶微分方程多点边值问题解的存在唯一性，主要利用和算子的不动点定理以及格林函数的性质，得到一类分数阶微分方程多点边值问题正解的存在唯一性，并且通过构造迭代序列来逼近此正解的结果，进而得出对此类边值问题正解的估计结论。作为应用，最后给出了一个例子。