一类Caputo分数阶p-Laplace反周期边值问题解的存在性

Existence of solutions to anti-periodic Caputo fractional boundary value problem with p-Laplacian operator

研究一类带有p-Laplace算子的Caputo分数阶微分方程反周期边值问题解的存在性.首先给出了所研究的分数阶边值问题的Green函数,并将研究Caputo分数阶p-Laplace微分边值问题解的存在性问题转化为研究一个非线性算子的不动点问题,然后利用Banach压缩映像原理和Schauder不动点定理得到边值问题解的存在性,最后,通过一个例子验证了本文的主要结果.

The existence of solutions to anti-periodic Caputo fractional boundary value problem withp-Laplacian operator is investigated in this paper. The green function of the anti-periodic Caputo fractionalboundary value problem is given, and it is proved that finding the solutions to the problem is equivalent tofinding the fixed points of the associated functional. Then, by means of the Banach＇s contraction mappingprinciple and Schauder fixed point theorem, some existence results are obtained. Finally, an example isprovided for illustrating the application of our main results.