A periodic boundary value problem of fractional differential equation involving $ p\left(t \right) $-Laplacian operator

The purpose of this article is to research the existence of solutions for fractional periodic boundary value problems with $ p\left(t \right) $-Laplacian operator. In this regard, the article needs to establish a continuation theorem corresponding to the above problem. By applying the continuation theorem, a new existence result for the problem is obtained, which enriches existing literature. In addition, we provide an example to verify the main result.