A time-nonlocal inverse problem for a hyperbolic equation with an integral overdetermination condition

This article is concerned with the study of unique solvability a timenonlocal inverse boundary value problem for second-order hyperbolic equation an integral overdetermination condition. To problem, we first reduce considered to auxiliary system trivial data and prove its equivalence (in certain sense) original problem. Then using Banach fixed point principle, existence uniqueness solution this shown. Further, on basis equivalency these problems theorem classical coefficient proved smaller time.