Recognition of a time-dependent source in a time-fractional wave equation

In the present paper, we deal with an inverse source problem for a time-fractional wave equation in a bounded domain in Rd. The time-dependent source is determined from an additional measurement in the form of integral over the space subdomain. The existence, uniqueness and regularity of a weak solution are obtained. A numerical algorithm based on Rothe's method is proposed, a priori estimates are proved and convergence of iterates towards the solution is established.