  In this paper, the initial-boundary value problems for the time-fractional
degenerate evolution equations are considered. Firstly, in the linear case, we
obtain the optimal rates of decay estimates of the solutions. The decay
estimates are also established for the time-fractional evolution equations with
nonlinear operators such as: p-Laplacian, the porous medium operator,
degenerate operator, mean curvature operator, and Kirchhoff operator. At the
end, some applications of the obtained results are given to derive the decay
estimates of global solutions for the time-fractional Fisher-KPP-type equation
and the time-fractional porous medium equation with the nonlinear source.
