分数阶积分微分方程多点边值问题解的存在性和唯一性

摘要

The existence and uniqueness of solutions were investigated for a class of multi-point boundary value problems of nonlinear integro-differential equations with fractional derivatives. Via calculating the Green's function and analyzing the properties of Green's function, the existence of solutions for multi-point boundary value problems was studied based on the Banach contraction,principle and by applying, the fixed point theorem. An example was given to illustrate the results.%研究一类非线性分数阶积分微分方程多点边值问题,通过计算边值问题的Green函数并分析Green函数的性质,利用压缩映射原理研究边值问题解的存在唯一性定理,并应用不动点定理得到了边值问题至少有一个解存在结论.同时给出了一个实例,说明所得结论.