A Priori Predictions for a Weak Solution to Time-Fractional Nonlinear Reaction-Diffusion Equations Incorporating an Integral Condition

Within this paper, we lay out the necessary criteria that ensure a solution’s presence and distinctiveness within a functionally weighted Sobolev space. This pertains to a specific group of initial-boundary value problems accompanied by an integral condition, all related to nonlinear partial fractional reaction-diffusion (RD) equations. Our findings are derived through the utilization of a priori estimates in Bouziani fractional spaces. By employing an iterative approach built upon outcomes from the linear counterpart, we successfully validate the existence and uniqueness of a weak generalized solution for the nonlinear conundrum.