What question did this study set out to answer?

This study aims to address the challenges of numerical differentiation in two-dimensional space with noisy data.

A Problem of Numerical Differentiation: Regularization by Fractional Laplacian

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Randomized trial introduces fractional Laplacian to enhance numerical differentiation outcomes, suggesting effectiveness over traditional methods.

This study aims to address the challenges of numerical differentiation in two-dimensional space with noisy data.
Proposed fractional Laplacian-based methods include the fractional Tikhonov method and iterated fractional Tikhonov method.
Theoretical error analysis was conducted to evaluate the proposed methods.
Numerical experiments were executed to demonstrate the effectiveness of these regularization approaches.
The fractional Tikhonov method showed improved regularization compared to classical solutions, effectively handling noise.
Numerical experiments confirmed the advantages of both fractional methods over traditional approaches.
The methods provide robust solutions for the ill-posed problem of numerical differentiation in the presence of noise.

Li et al. (2026) studied this question.

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Randomized trial introduces fractional Laplacian to enhance numerical differentiation outcomes, suggesting effectiveness over traditional methods.