Abstract
In this paper, a concentration identification problem of the time fractional inhomogeneous diffusion equation (TFIDE) is investigated. The TFIDE is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order . Our purpose is to recover the solute concentration from source measurement and boundary data. We show that this problem is severely ill-posed and further apply a convolution-type regularization method to solve it. Convergence estimates are given under a priori bound assumptions for the exact solution. Finally, we provide two numerical examples to confirm our theoretical analysis and show that the corresponding numerical method works effectively.
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