Identifying a space-dependent source term in distributed order time-fractional diffusion equations

The aim of this paper is to investigate an inverse problem recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such ill-posed and has important practical applications. For problem, we propose general regularization method based on the idea filter method. With suitable condition, prove that optimal under various choices parameter. One priori parameter choice rule another one discrepancy principle. Finally, capabilities our are illustrated both Tikhonov Landweber