Abstract: By using the fountain theorem in critical point theory and the theory of fractional variable exponent Sobolev space, the author gave the existence of infinitely many high energy solutions of fractional Kirchhofftype equation with p(x)-Laplacian operator, without assuming that the (AR) type superlinear condition held.

Key words: Kirchhofftype equation, fractional differential equation, high energy solution, critical point, p(x)-Laplacian operator