  We prove an existence result for the fractional Kelvin-Voigt's model
involving Caputo's derivative on time-dependent cracked domains. We first show
the existence of a solution to a regularized version of this problem. Then, we
use a compactness argument to derive that the fractional Kelvin-Voigt's model
admits a solution which satisfies an energy-dissipation inequality. Finally, we
prove that when the crack is not moving, the solution is unique.
