INVERSE SOURCE PROBLEM FOR A SEMILINEAR FRACTIONAL DIFFUSION-WAVE EQUATION UNDER A TIME-INTEGRAL CONDITION

We study the inverse boundary value problem on determining a space-dependent component in right-hand side of semilinear time fractional diffusion-wave equation. find sufficient conditions for time-local uniqueness solution under time-integral additional condition \[\frac{1}{T}\int_{0}^{T}u(x,t)\eta_1(t)dt=\Phi_1(x), \;\;\;x\in \Omega\subset \Bbb R^n\] where $u$ is unknown first such equation, $\eta_1$ and $\Phi_1$ are given functions. use method Green's function.