  An initial-boundary value problem for a time-fractional subdiffusion equation
with the Riemann-Liouville derivatives on N-dimensional torus is considered.
The uniqueness and existence of the classical solution of the posed problem are
proved by the classical Fourier method. Sufficient conditions for the initial
function and for the right-hand side of the equation are indicated, under which
the corresponding Fourier series converges absolutely and uniformly. It should
be noted, that the condition on the initial function found in this paper is
less restrictive than the analogous condition in the case of an equation with
derivatives in the sense of Caputo

Analysis of PDEs