Reconstruct the unknown source on the right hand side of time fractional diffusion equation with Caputo-Hadamard derivative

The Caputo-Hadamard derivative was used to investigate the problem of functional recovery in this study. This problem is ill-posed, we propose a novel Quasi-reversibility for reconstructing the sought function and show that the regularization solution depends on space. After that, the convergence rates are established under a priori and posterior choice rules of regularization parameters, respectively.