INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION

Abstract

The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.