Abstract: By using a bootstrap argument method, we considered the global existence for the solution of a class of fractional Hartree equations with timedependent damping/gain. We discussed the global existence condition of the solution from two aspects of the damping/gain coefficients and the initial value, respectively. We obtained a global existence condition of the fractional Hartree equation which only depends on the damping/gain coefficients and only depends on the initial value of the solution.

Key words: damping/gain, global existence, fractional Hartree equation