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In this paper, we study the ill-posed fractional backward heat equation ⎧⎨⎩ ∂γ u ∂t γ = Δu, x ∈ Rn, t ∈ (0, T ), u(x, T ) = ϕ(x), x ∈ Rn, where ϕ is unknown exact data and only noisy data ϕε with ϕε(·) − ϕ(·)L2(Rn)  ε is available. The problem is regularized by the well-posed mollified problem ⎧⎨⎩ ∂γ vν ∂t γ = Δvν, x ∈ Rn, t ∈ (0, T ), vν(x, T ) = Sν(ϕε(x)), x ∈ Rn, where ν > 0 and Sν(ϕε(x)), a mollification of ϕε defined by the convolution of ϕε(x) with Dirichlet kernel. The error estimates u(·, t) − vν(·, t)H l(Rn), 0 ≤ l are established for ν chosen a priori and a posteriori.