AbstractThis paper studies an inverse source problem for a time fractional diffusion equation with the distributed order Caputo derivative.
The space-dependent source term is recovered from a noisy final data.
The uniqueness, ill-posedness and a conditional stability for this inverse source problem are obtained.
The inverse problem is formulated into a minimization functional with Tikhonov regularization method.
Further, based on the series representation of the regularized solution, we give convergence rates of the regularized solution under an a-priori and an a-posteriori regularization parameter choice rule.
With an adjoint technique for computing the gradient of the regularization functional, the conjugate gradient method is applied to reconstruct the space-dependent source term.
Two numerical examples illustrate the effectiveness of the proposed method.