RAVSHAN ASHUROV AND MARJONA SHAKAROVAАннотация. The Schrödinger equation i∂ ρ t u(x, t) − uxx(x, t) = p(t)q(x) + f (x, t) ( 0 < t ≤ T, 0 < ρ < 1), with the Riemann-Liouville derivative is considered. An inverse problem is investigated in which, along with u(x, t), also a time-dependent factor p(t) of the source function is unknown. To solve this inverse problem, we take the additional condition B[u(•, t)] = ψ(t) with an arbitrary bounded linear functional B. Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained. The applied method allows us to study a similar problem by taking instead of d 2 /dx 2 an arbitrary elliptic differential operator A(x, D), having a compact inverse.