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This paper is concerned with the study of the well-posedeness for the initialboundary value problem to the time-fractional wave equation with acousticboundary conditions. The problem is considered in a bounded and connecteddomain $\Omega \subset {\mathbb{R}^{n}}$, $n \geq 2$, which includes simplyconnected regions. The boundary of $\Omega$ is made up of two disjoint pieces$\Gamma_{0}$ and $\Gamma_{1}.$ Homogeneous Dirichlet conditions are enforced on$\Gamma_0$, while acoustic boundary conditions are considered on $\Gamma_1$. Toestablish our main result, we employ the Faedo-Galerkin method and successfullysolve a general system of time-fractional ordinary differential equations whichextends the scope of the classical Picard-Lindel\"of theorem.

On the Initial Boundary Value Problem to the Time-Fractional Wave Equation with Acoustic Boundary Conditions