An undetermined coefficient problem for a fractional diffusion equation

We consider a fractional diffusion equation (FDE) with an undetermined time-dependent diffusion coefficient a(t). Firstly, for the direct problem part, we establish the existence, uniqueness and some regularity properties of the weak solution for this FDE with a fixed Secondly, for the inverse problem part, in order to recover we introduce an operator and show its monotonicity. With this property, we establish the uniqueness of a(t) and create an efficient reconstruction algorithm to recover this coefficient.

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