Abstract multi-term fractional differential equations

Abstract

The present paper is an addendum to our recent work on abstract time-fractional equations of the following form: where nεℕ\{1}, A and A1,., An-1are 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 Dαtdenotes 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.