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.