## Determining a time-dependent coefficient in a time-fractional diffusion-wave equation with the Caputo derivative by an additional integral condition.(English)Zbl 1479.35957

Summary: This paper is devoted to recovering a time-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation with the time Caputo derivative from an additional integral condition. The uniqueness and a conditional stability for such an inverse problem are proved. Then the two-point gradient method is used to solve the inverse zeroth-order coefficient problem numerically. Some properties of the forward operator are obtained, such as the Fréchet differentiability, the Lipschitz continuity and the tangential cone condition to guarantee the convergence of the proposed algorithm. Four numerical examples in one-dimensional and two-dimensional spaces are provided to show the effectiveness and stability of the suggested algorithm.

### MSC:

 35R30 Inverse problems for PDEs 35L20 Initial-boundary value problems for second-order hyperbolic equations 35R11 Fractional partial differential equations 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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