Necessary non-local conditions for a diffusion-wave equation

In this article, diffusion-wave equation with fractional derivative in Riemann–Liouville sense is investigated. Integral operators with the Write function in the kernel associated with the investigational equation are introduced. In terms of these operators necessary non-local conditions binding traces of solution and its derivatives on the boundary of a rectangular domain are found. Necessary non-local conditions for the wave are obtained by using the limiting properties of Write function. By using the integral operator's properties the theorem of existence and uniqueness of solution of the problem with integral Samarski's condition for the diffusion-wave equation is proved. The solution is obtained in explicit form.