Identification of time-dependent convection coefficient in a time-fractional diffusion equation

In the present paper, we devote our effort to solve a nonlinear inverse problem for identifying a time-dependent convection coefficient in a time-fractional diffusion equation from the measured data at an interior point for one-dimensional case. We prove the existence, uniqueness and regularity of solution for the direct problem by using the fixed point theorem. The stability of inverse convection coefficient problem is obtained based on the regularity of solution for the direct problem and some generalized Gronwall's inequalities. We use a modified optimal perturbation regularization algorithm to solve the inverse convection coefficient problem. Two numerical examples are provided to show the effectiveness of the proposed method.