The existence of ground state solutions for a class of fractional elliptic partial differential equations with nonlocal terms by variational methods was investigated. Firstly, it was shown that the functional was coercive and bounded from below Nehari manifold, and thus there existed a sequence of bounded miniaturization. Secondly, it was proved that the sequence was a (PS)_c sequence by Ekeland's principle. In addition, the functional was proved to satisfy the (PS)_c condition in combination with the assumptions. Finally, the existence of the base state solution of this class of problems was obtained.