Abstract
The aim of this research is to demonstrate the existence and the uniqueness of the weak solution for a semilinear fractional parabolic problem with the special case of the second integral boundary condition. For this aim, we split the proof into two parts; to study the main linear problem part, we used the variable separation method, and concerning the semilinear problem part, we apply an iterative method and a priori estimate for the study of the weak solution.