Determination of time-dependent coefficient in inverse coefficient problem of fractional wave equation

This article investigates a one-dimensional inverse coefficient problem of determining time-dependent coefficient in the time-fractional wave equation using initial and homogenous Dirichlet boundary conditions under additional condition. Stable explicit finite difference scheme (EFDS for short) is used to construct numerical solution of the time fractional wave equation subject to homogenous Dirichlet boundary conditions. Afterward, since the problem is generally ill-posed, the Tikhonov's regularization technique is applied to obtain a uniform constant result. By von Neumann and Lax–Richtmyer theorems, the stability and convergence of the fractional scheme are proved. In the end, a numerical test example explain that the proposed method is stable and works well for different noise levels.