Coefficient inverse problem for a fractional diffusion equation

In this paper, we consider an initial/boundary value problem for a fractional diffusion equation in a bounded domain Ω: where is the Caputo derivative and 0 < α < 2, α ≠ 1. We discuss an inverse problem of determining spatial coefficient p(x), x ∈ Ω and/or order α of the fractional derivative by data u|ω × (0, T), where ω⊂Ω is a sub-domain. Our main result is the uniqueness under conditions where the initial value is positive and ω is a neighbourhood of ∂Ω. The proof is done by transforming the solution u to the solution of the wave equation.

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