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Theory and Applications of an Inverse Source Problem for Anomalous Diffusion Processes |
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PP: 705-712 |
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doi:10.18576/pfda/110406
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Author(s) |
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Fadi Awawdeh,
Mona Khandaqji,
Rafat Alshorman,
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Abstract |
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| This work investigates an inverse problem associated with fractional diffusion equations in the setting of Banach spaces, with particular emphasis on identifying a time-dependent source term from overspecified data. We rigorously establish existence, uniqueness, and regularity results for both classical and strong solutions by employing perturbation techniques and the theory of strongly continuous semigroups. The proposed theoretical framework accommodates a broad class of linear operators, including sectorial and elliptic types, thereby ensuring wide applicability to models in physics and engineering. To demonstrate the practical relevance of our approach, we apply it to fractional heat transfer problems and the time-fractional Boltzmann equation, which models anomalous neutron transport. The findings advance the theoretical foundation of inverse source problems in fractional systems and offer robust tools for the unique recovery of source terms in anomalously diffusive media. |
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