Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients

We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. First, we show some results on the unique existence of solution to time-fractional ordinary differential equations. Then the unique existence of weak and strong solutions to a time-fractional partial differential equation is derived by using the Galerkin method.