An inverse source time-fractional diffusion problem via an input-output mapping
Keywords:inverse source problem, time-fractional diffusion equation, Riemann-Liouville fractional derivative, input-output mapping, distinguishability
In this paper, we investigate an inverse source problem involving a one-dimensional diffusion equation of a time-fractional RiemannLiouville derivative with 0 < α < 1. First, results on the existence and regularity of the weak solution of the direct problem are obtained. For the determination of the unknown time-dependent source term, we use a monotone and distinguishable input-output mapping defined by the additional over-determination integral data for the considered sub-diffusion problem. Finally, the uniqueness of the solution of the inverse problem is proved.
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