  In this paper we investigate the solution of generalized distributed order
diffusion equations with composite time fractional derivative by using the
Fourier-Laplace transform method. We represent solutions in terms of infinite
series in Fox $H$-functions. The fractional and second moments are derived by
using Mittag-Leffler functions. We observe decelerating anomalous subdiffusion
in case of two composite time fractional derivatives. Generalized uniformly
distributed order diffusion equation, as a model for strong anomalous behavior,
is analyzed by using Tauberian theorem. Some previously obtained results are
special cases of those presented in this paper.
