What question did this study set out to answer?

To identify the unknown temporal component of the source term in a time-fractional diffusion equation from spatial measurements.

February 2, 2026MathematicsOpen Access

An Inverse Source Problem in a Variable-Order Time-Fractional Diffusion PDE

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Authors

MSMarián SlodičkaGhent University

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Implication

This analysis demonstrates the well-posedness of an inverse source problem in a time-fractional diffusion equation, indicating potential in mathematical modeling.

Key Points

To identify the unknown temporal component of the source term in a time-fractional diffusion equation from spatial measurements.
Analyzed a semilinear diffusion equation with a Caputo-type time-fractional derivative.
Considered the problem in a bounded Lipschitz domain with homogeneous Dirichlet boundary conditions.
Established existence and uniqueness results in suitable function spaces.
Demonstrated well-posedness of the inverse source problem.
Showed that the unknown function can be effectively identified from localized measurements.

Cite This Study

Marián Slodička (2026) studied this question.

synapsesocial.com/papers/6980fed9c1c9540dea8115b6 https://doi.org/10.3390/math14030488

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Implication

This analysis demonstrates the well-posedness of an inverse source problem in a time-fractional diffusion equation, indicating potential in mathematical modeling.

An Inverse Source Problem in a Variable-Order Time-Fractional Diffusion PDE

Discussion

Member takes

Implication

Key Points

Cite This Study

An Inverse Source Problem in a Variable-Order Time-Fractional Diffusion PDE

Discussion

Member takes

Implication

Key Points

Cite This Study

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