  In this paper, we investigate the numerical approximation of Hamilton-Jacobi
equations with the Caputo time-fractional derivative. We introduce an explicit
in time discretization of the Caputo derivative and a finite difference scheme
for the approximation of the Hamiltonian. We show that the approximation scheme
so obtained is stable under an appropriate condition on the discretization
parameters and converges to the unique viscosity solution of the
Hamilton-Jacobi equation.
