Fractional diffusion equation with discretely distributed differentiation operator

摘要

We discuss an initial value problem for a fractional diffusionequation with discretely distributed fractional differentiation operatorwith respect to time variable. We construct a fundamental solution ofthe 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–Nersesyanoperator, and the corresponding results for equations with Caputo andRiemann–Liouville derivatives are particular cases of proved assertions.