What question did this study set out to answer?

The study aims to determine spatially varying source terms in diffusion equations using integral measurements.

Local Solvability for an Inverse Source Problem for Nonlocal Diffusion Equations With Variable Order

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Investigates solving for source terms in diffusion equations, suggesting effective techniques and algorithms for improvement.

The study aims to determine spatially varying source terms in diffusion equations using integral measurements.
Constructed an integral equation linking unknown sources and observations
Utilized Mittag-Leffler functions for analysis
Applied the Fredholm alternative for existence and uniqueness of solutions
Developed a Tikhonov regularization algorithm for improved accuracy
Demonstrated the existence and uniqueness of solutions for the forward problem
Validated the performance of the proposed algorithm in accuracy and efficiency through numerical experiments

Tang et al. (2026) studied this question.

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