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Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions. (English) Zbl 1459.35395

Summary: In this paper, an inverse problem of determining a time-dependent source term in a one-dimensional time-fractional diffusion equation from the energy measurement is studied. This problem is obtained from a classical diffusion problem by replacing the time derivative with a fractional derivative. The well-posedness of the inverse problem is shown by using eigenfunction expansion of a non-self adjoint spectral problem along the generalized Fourier method.

MSC:

35R30 Inverse problems for PDEs
35R11 Fractional partial differential equations
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