Determination of a time dependent source in semilinear pseudoparabolic equations with Caputo fractional derivative

This paper devoted to study unique solvability of inverse source problem for a semilinear time fractional pseudoparabolic equation perturbed by a damping term. Inverse problem consists of recovering a solely time dependent coefficient of right-hand side under a measurement in an integral form. The damped term acts in the equation as a nonlinear source or as an absorption, depending on its sign of coefficient, where it is positive or negative, respectively. In these both cases, we have established sufficient conditions on data, where the inverse problem has a global or local in time unique weak and strong solution.