What question did this study set out to answer?

This research aims to determine the initial conditions and source terms in a time-fractional diffusion equation using limited measurements.

Uniqueness and non-uniqueness for an inverse source problem of a distributed order time-fractional diffusion equation

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Investigating an inverse source problem, findings reveal conditions for uniqueness in measurements, highlighting temporal diversity.

This research aims to determine the initial conditions and source terms in a time-fractional diffusion equation using limited measurements.
Investigated an inverse source problem related to a distributed order time-fractional diffusion equation.
Analyzed uniqueness conditions based on measurements at fixed time instances and spatial domains.
Established conditional uniqueness under specific assumptions regarding observation times.
Single time measurement is insufficient for guaranteeing uniqueness in the problem.
Two distinct time measurements provide a unique solution for unknowns within a subdomain under certain conditions.
Highlight the importance of temporal diversity for restoring identifiability with limited spatial observations.

Dinh Nguyen Duy Hai (2026) studied this question.

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