INITIAL-BOUNDARY VALUE PROBLEM FOR A SUBDIFFUSION EQUATION WITH CAPUTO DERIVATIVE

We investigate an initial-boundary value problem for a time-fractional subdiffusion equation with the Caputo derivatives on $N$-dimensional torus by classical Fourier method. Since our solution is established eigenfunction expansion of elliptic operator, method proposed in this article can be used to arbitrary domain and operator variable coefficients. It should noted that conditions existence found cannot weakened, provides corresponding example.