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Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data

Abstract Two inverse problems with final overdetermination for diffusion and wave equations containing the Caputo fractional time derivative and a fractional Laplacian of distributed order are considered. They are: 1) the problem to reconstruct a time-dependent source term; 2) the problem to recover simultaneously the source term, the order of the time derivative and the fractional Laplacian. Uniqueness of solutions of these problems is proved. Sufficient conditions for the uniqueness are stricter for the 2nd problem than for the 1st problem.