What question did this study set out to answer?

This work focuses on reconstructing the initial condition of a parabolic equation from noisy data.

Regularization Methods Based on a Priori Information for Backward Inhomogeneous Caputo Time‐Fractional Parabolic Equation

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Randomized trial addresses inverse problem for parabolic equations, suggesting improved methods for stability.

This work focuses on reconstructing the initial condition of a parabolic equation from noisy data.
Introduced two Tikhonov-type regularization frameworks for stability.
Established error estimates for regularized solutions, including Hölder-type and logarithmic types.
Conducted numerical experiments using finite element discretization and minimization algorithms.
Hölder-type estimates show improvement in specific parameter regimes.
Sharp error estimates confirm the stability of the approximation.
Numerical experiments validate theoretical results effectively.

Duc et al. (2026) studied this question.

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