  Inverse problem for multi-term fractional parabolic equation in two
dimensional space, involving m + 1 Caputo fractional derivatives in time, is
investigated. Presence of nonlocal boundary conditions leads to a
non-self-adjoint spectral problem. A bi-orthogonal system of functions is used
to construct the solution that involves double infinite series. Properties of
multinomial Mittag-Leffler function and eigenfunctions are used to prove the
classical nature of the solution under certain regularity conditions on the
given datum.
