An Inverse Initial Value Problem For A Time Fractional Diffusion Wave Equation

In this study,we consider a.n inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion wave equation.By using some additional boundary measured data,the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique.The inverse problem is formulated to solve a Tikhonov type optimization problem by using a finite dimensional approximation.We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.