Fractional diffusion equation with discretely distributed differentiation operator

We discuss an initial value problem for a fractional diffusion equation with discretely distributed fractional differentiation operator with respect to time variable. We construct a fundamental solution of the considered equation, give a solution of the problem under study, and prove a uniqueness theorem in the class of rapid growth functions. The fractional differentiation is given by the Dzhrbashyan–Nersesyan operator, and the corresponding results for equations with Caputo and Riemann–Liouville derivatives are particular cases of proved assertions.