  A generalized Langevin equation with fluctuating diffusivity (GLEFD) is
proposed, and it is shown that the GLEFD satisfies a generalized
fluctuation-dissipation relation. If the memory kernel is a power law, the
GLEFD exhibits anomalous subdiffusion, non-Gaussianity, and
stretched-exponential relaxation. The case in which the memory kernel is given
by a single exponential function is also investigated as an analytically
tractable example. In particular, the mean-square displacement and the
self-intermediate-scattering function of this system show plateau structures. A
numerical scheme to integrate the GLEFD is also presented.
