Abstract
Abstract The main objective of this paper is to address the backward problem in the distributed-order time-space fractional diffusion equation (DTSFDE) with Neumann boundary conditions using final data. We began by employing the Finite Difference Method (FDM) combined with matrix transformation techniques to compute the direct problem of DTSFDE. Subsequently, by using the Tikhonov regularization method, the inverse problem is transformed into a variational problem. With the help of the derived sensitivity and adjoint problems, the conjugate gradient algorithm is employed to find an approximate solution for the initial data. Finally, through numerical examples in one and two dimensions, we demonstrated the effectiveness and stability of this method, further verifying its reliability in practical applications.
Published Version
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