Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions
Keyword(s):
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.
2020 ◽
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