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This study investigates the inverse problem of determining the right-handside of a telegraph equation given in a Hilbert space. The main equation underconsideration has the form $(D_{t}^{\rho})^{2}u(t)+2\alphaD_{t}^{\rho}u(t)+Au(t)=p( t)q+f(t)$, where $0<t\leq T$, $0<\rho<1$ and$D_{t}^{\rho}$ is the Caputo derivative. The equation contains a self-adjointpositive operator $A$ and a time-varying multiplier $p(t)$ in the sourcefunction, which, like the solution of the equation, is unknown. To solve theinverse problem, an additional condition $B[u(t)] = \psi(t)$ is imposed, where$B$ is an arbitrary bounded linear functional. The existence and uniqueness ofa solution to the problem are established and stability inequalities arederived. It should be noted that, as far as we know, such an inverse problemfor the telegraph equation is considered for the first time. Examples of theoperator $A$ and the functional $B$ are discussed.

Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative