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In a Banach space, the inverse source problem for a fractional differential equation with Caputo–Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements fromD  ⁢   (  A  ){D(A)}   , and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator  A  is a generator of positive and compact semigroup the uniqueness, existence and stability of the solution are proved.

Inverse source problem for the abstract fractional differential equation