The fundamental solution of a diffusion-wave equation of fractional order

We construct a fundamental solution of a diffusion-wave equation with Dzhrbashyan-Nersesyan fractional differentiation operator with respect to the time variable. We prove reduction formulae and solve the problem of sign-determinacy for the fundamental solution. A general representation for solutions is constructed. We give a solution of the Cauchy problem and prove the uniqueness theorem in the class of functions satisfying an analogue of...