  In this paper the Green formula for the operator of fractional
differentiation in Caputo sense is proved. By using this formula the integral
representation of all regular in a rectangular domains solutions is obtained in
the form of the Green formula for operator generating the time-fractional
telegraph equation. The unique solutions of the initial-boundary value problem
with boundary conditions of first kind is constructed. The proposed approach
can be used to study the more general evolution FPDE as well as ODE with Caputo
derivatives.
