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The paper considers an inverse source problem for a one-dimensionaltime-fractional heat equation with the generalized impedance boundarycondition. The inverse problem is the time dependent source parameteridentification together with the temperature distrubution from the energymeasurement. The well-posedness of the inverse problem is shown by applying theFourier expansion in terms of eigenfunctions of a spectral problem which hasthe spectral parameter also in the boundary condition and by using the resultson Volterra type integral equation with the kernel may have a diagonalsingularity.

Inverse source problem for a time-fractional heat equation with generalized impedance boundary condition