On some initial - boundary value problems for the parabolic equations with the initial operators of fractional order.

In the present paper, we study an initial-boundary problem for the parabolic equation ∂/∂t μ (x, t) + A (x, D) μ (x, t) = 0 with general elliptic operator and with the fractional initial conditions. Here A (x, D) non negative elliptic operator which defined in any N dimensional domain Ω with the smooth boundary. We prove the existence and uniqueness of the solution of the problem. In particular, initial conditions can be given through the one-sided Marchaud, Grunwald-Letnikov or Liouville-Weyl fractional derivatives. [ABSTRACT FROM AUTHOR]