Variational formulation of time-fractional parabolic equations

Abstract: We consider initial/boundary value problems for time-fractional parabolic PDE of order $0<\alpha<1$ with Caputo fractional derivative (also called fractional diffusion equations in the literature). We prove well-posedness of corresponding variational formulations based entirely on fractional Sobolev-Bochner spaces, and clarify the question of possible choices of the initial value.