Sidi, H. ouldZaky, M. A.EL Waled, K.Akgul, A.Hendy, A. S.2024-12-242024-12-2420231221-14511841-8759https://doi.org/10.59277/RomRepPhys.2023.75.120https://hdl.handle.net/20.500.12604/7905In this paper, we consider the problem of identifying the unknown source function in the time-space fractional diffusion equation from the final obser-vation data. An implicit difference technique is proposed in conjunction with the matrix transfer scheme for approximating the solution of the direct problem. The challenge pertains to an inverse scenario encompassing a nonlocal ill-posed operator. The problem under investigation is formulated as a regularized optimization problem with a least-squares cost function minimization objective. An approximation for the source function is obtained using an iterative non-stationary Tikhonov regularization approach. Three numerical examples are reported to verify the efficiency of the pro-posed schemes.eninfo:eu-repo/semantics/openAccessTime-space fractional equationInverse problemFractional Lapla-cianIterative non-stationary Tikhonov regularizationArticle754Q2WOS:001110490400009Q22-s2.0-8517553137210.59277/RomRepPhys.2023.75.120