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Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions

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Abstract
In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order. More specifically, we discuss the uniqueness of a solution when reconstructing a space-dependent source from a time-averaged measurement, or a final in time measurement. Weakly singular solutions are included in the class of admissible solutions. The obtained results are also valid if the order of the fractional derivative is constant.
Keywords
Statistics and Probability, Statistical and Nonlinear Physics, Analysis

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MLA
Van Bockstal, Karel. “Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions.” FRACTAL AND FRACTIONAL, vol. 5, no. 4, 2021, doi:10.3390/fractalfract5040169.
APA
Van Bockstal, K. (2021). Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions. FRACTAL AND FRACTIONAL, 5(4). https://doi.org/10.3390/fractalfract5040169
Chicago author-date
Van Bockstal, Karel. 2021. “Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions.” FRACTAL AND FRACTIONAL 5 (4). https://doi.org/10.3390/fractalfract5040169.
Chicago author-date (all authors)
Van Bockstal, Karel. 2021. “Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions.” FRACTAL AND FRACTIONAL 5 (4). doi:10.3390/fractalfract5040169.
Vancouver
1.
Van Bockstal K. Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions. FRACTAL AND FRACTIONAL. 2021;5(4).
IEEE
[1]
K. Van Bockstal, “Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions,” FRACTAL AND FRACTIONAL, vol. 5, no. 4, 2021.
@article{8725287,
  abstract     = {{In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order. More specifically, we discuss the uniqueness of a solution when reconstructing a space-dependent source from a time-averaged measurement, or a final in time measurement. Weakly singular solutions are included in the class of admissible solutions. The obtained results are also valid if the order of the fractional derivative is constant.}},
  articleno    = {{169}},
  author       = {{Van Bockstal, Karel}},
  issn         = {{2504-3110}},
  journal      = {{FRACTAL AND FRACTIONAL}},
  keywords     = {{Statistics and Probability,Statistical and Nonlinear Physics,Analysis}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{11}},
  title        = {{Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions}},
  url          = {{http://dx.doi.org/10.3390/fractalfract5040169}},
  volume       = {{5}},
  year         = {{2021}},
}

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