identification of source term in time-fractional diffusion equations

In this paper, we propose a numerical method for the inverse problem of identifying the source term of a time fractional diffusion equation from noisy internal observations. such problem can arise in a diverse set of areas with many applications in environmental engineering, hydrology, and physics. using separation of variables method, we construct a formal series solution of the direct problem which allows us to obtain a computational formula for the unknown source term. upon discretization, the resulted illconditioned system defining the inverse solution is solved using tikhonov regularization. some examples are given to validate the efficiency and reliability of the proposed method.