Abstract multi-term fractional differential equations

The present paper is an addendum to our recent work on abstract time-fractional equations of the following form: 0.1 DantU(t) + Σn-1 i=1 Ai D ai tU(t) = AiDatU(t) + F(t),t > 0, u(k) 0 = uk , k = 0, • • • [αn] - 1, ℕ where n є ℕ \ {1}, A and A1, • • •, An-1 are closed linear operators on a sequentially complete locally convex space X, 0 ≤ α1 < • • • < αn, 0 ≤ α < αn, f (t) is an X-valued function, and denotes the Caputo fractional derivative of order α [2]. We analyze the existence and uniqueness of solutions of the equation (0.1), and prove a Ljubich type uniqueness theorem in this context.