A priori estimates for weak solution for a time-fractional nonlinear reaction-diffusion equations with an integral condition

In this paper, we establish sufficient conditions for the existence and uniqueness of the solution in functional weighted Sobolev space for a class of initial-boundary value problems with integral condition for a class of nonlinear partial fractional reaction-diffusion (RD) equations. The results are established by using a priori estimate in Bouziani fractional spaces and applying an iterative process based on results obtained for the linear problem, we prove the existence, uniqueness of the weak generalized solution of the nonlinear problem.